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Subject:	Mathematics
Topic:	Calculus
Views:	228,921

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Name:	integralCALC Academy (integralCALC)
Type:	Individual

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Instructor

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Krista King

Calculus II

Video Lectures

Displaying all 176 video lectures.

Lecture 1 Play Video	Area Under the Curve (Example 1) In this video, Krista King from integralCALC Academy shows how to find the area under the curve using elementary area computations. Looks at left endpoints, right endpoints, and midpoints.
Lecture 2 Play Video	Area Under the Graph vs. Area Enclosed by the Graph In this video, Krista King from integralCALC Academy compares the area under the graph vs. the area enclosed by the graph (Calculus problem example).
Lecture 3 Play Video	Summation Notation: Finding the Sum In this video, Krista King from integralCALC Academy explains a summation notation for finding the sum (Calculus problem example).
Lecture 4 Play Video	Summation Notation: Expanding In this video, Krista King from integralCALC Academy explains a summation notation by expanding (Calculus problem example).
Lecture 5 Play Video	Summation Notation: Collapsing In this video, Krista King from integralCALC Academy explains a summation notation by collapsing (Calculus problem example).
Lecture 6 Play Video	Riemann Sums Right Endpoints In this video, Krista King from integralCALC Academy shows how to use Riemann Sums and right endpoints to evaluate the area under the curve.
Lecture 7 Play Video	Riemann Sums Midpoints In this video, Krista King from integralCALC Academy shows how to use Riemann Sums and midpoints to evaluate the area under the curve.
Lecture 8 Play Video	Trapezoidal Rule In this video, Krista King from integralCALC Academy talks about the Trapezoidal Rule (Calculus example).
Lecture 9 Play Video	Simpson's Approximation In this video, Krista King from integralCALC Academy talks about Simpson's Approximation (Calculus problem example).
Lecture 10 Play Video	Definite Integral In this video, Krista King from integralCALC Academy discusses Definite Integral (Calculus help).
Lecture 11 Play Video	Definite Integral of an Even Function In this video, Krista King from integralCALC Academy shows how to calculate the definite integral of an even function on the range -a to a. We'll confirm that the function is even by plugging -x for x into our function and seeing that we get back the original function. Then we'll simplify the definite integral by changing the range from -a to a to 0 to a, but multiplying the integral by 2. Then, we'll simplify and evaluate the definite integral.
Lecture 12 Play Video	Definite Integral of an Odd Function In this video, Krista King from integralCALC Academy shows how to calculate the definite integral of an odd function. If the range of the definite integral is -a to a, and if the function is odd, then the value of the integral is 0. To determine if the function is odd, plug -x in for x, and then simplify. If the result is -f(x), then the function is odd. Since the integral is supposed to be evaluated from -a to a, and that the function is odd, you know that the function is symmetric about the origin, and therefore that the positive area will cancel out the negative area and that the value of the integral will be 0.
Lecture 13 Play Video	Fundamental Theorem of Calculus (Part I) In this video, Krista King from integralCALC Academy talks about the Fundamental Theorem of Calculus (Calculus problem example).
Lecture 14 Play Video	Fundamental Theorem of Calculus (Part II) In this video, Krista King from integralCALC Academy shows how to use the fundamental theorem of calculus.
Lecture 15 Play Video	Indefinite Integrals In this video, Krista King from integralCALC Academy talks about Indefinite Integrals (Calculus example).
Lecture 16 Play Video	Properties of integrals In this video, Krista King from integralCALC Academy shows how to use the properties of integrals to simplify a definite integral. When you have the sum or difference of two terms in an integral, you can separate them into two separate integrals. When all terms inside the integral are part of one product or quotient, you can pull a constant coefficient out in front of the integral to simplify it. When you evaluate two definite integrals on the same range, you can evaluate them together or separately.
Lecture 17 Play Video	Find f(x) Given f''(x), its Second Derivative In this video, Krista King from integralCALC Academy shows how to find the original function, f(x), given f''(x), its second derivative, also called f double prime of x. Work backwards and take the integral of f''(x) to get the first derivative, f'(x), then take the integral of f'(x) to get the original function, f(x). Make sure to add a constant of integration each time.
Lecture 18 Play Video	Find f Given f'' and Initial Conditions In this video, Krista King from integralCALC Academy shows how to find f(x), the original function, given f''(x), f double prime of x, or the second derivative of f, and initial conditions. Take the integral of f''(x) to get f'(x), then take the integral of f'(x) to get f(x). Make sure to add the constant of integration after each integration, then plug in both initial conditions to f(x). This will give you a system of equations that you can solve for both constants of integration.
Lecture 19 Play Video	Find f(x) Given f'''(x), its Third Derivative In this video, Krista King from integralCALC Academy shows how to find the original function, f(x), given f'''(x), its third derivative, also called f triple prime of x. Work backwards and take the integral of f'''(x) to get the second derivative, f''(x), then take the integral of f''(x) to get the first derivative, f'(x), then take the integral of f'(x) to get the original function, f(x). Make sure to add a constant of integration each time.
Lecture 20 Play Video	Integral of a Quadratic Function In this video, Krista King from integralCALC Academy shows how to calculate the integral of a quadratic function by completing the square. To complete this problem, you'll need to complete the square of the quadratic, then use trigonometric substitution to calculate the integral. Once you've used trigonometric substitution to simplify the integral, you'll use integration by parts to simplify further. Finally, you'll back substitute to get the answer in terms of x instead of theta. In order to do this, you'll need to use the values from the right triangle you drew when you set up your trigonometric substitution problem.
Lecture 21 Play Video	Initial Value Problem In this video, Krista King from integralCALC Academy talks about the Initial Value Problem (Calculus example).
Lecture 22 Play Video	U-Substitution In this video, Krista King from integralCALC Academy shows how to do U-Substitution (Calculus example).
Lecture 23 Play Video	U-Substitution in Definite Integrals In this video, Krista King from integralCALC Academy shows how to do U-Substitution in Definite Integrals (Calculus problem example).
Lecture 24 Play Video	U-Substitution with Integration by Parts In this video, Krista King from integralCALC Academy shows how to find the integral of a function using u-substitution and then integration by parts. Also, since this is a definite integral, evaluate at the limits of integration.
Lecture 25 Play Video	Integration by Parts In this video, Krista King from integralCALC Academy talks about Integration by Parts (Calculus example).
Lecture 26 Play Video	Integration by Parts Two Times In this video, Krista King from integralCALC Academy shows how to use the integration by parts formula to find the integral of a function involving the exponential (e^x) and a trigonometric function. To complete this problem, you'll need to identify which part of the function will be set equal to u, and which part of the function will be set equal to dv. Then you'll take the derivative of u to find du and take the integral of dv to find v. Then you'll plug u, du, v and dv into your integration by parts formula. With this particular problem, you'll have to perform a second round of integration by parts. After using integration by parts twice, you'll have to move the remaining integral from the right hand side to the left hand side, and then divide both sides by the coefficient from the left hand side in order to solve for the original integral.
Lecture 27 Play Video	Integration by Parts Three Times In this video, Krista King from integralCALC Academy shows how to use the integration by parts formula three times in a row in order to simplify and evaluate the integration of a function. In this particular problem, we'll evaluate the integral of the product of a power function and an exponential function.
Lecture 28 Play Video	Integration by Parts to Prove the Reduction Formula In this video, Krista King from integralCALC Academy shows how to use integration by parts to prove a reduction formula.
Lecture 29 Play Video	Tabular Integration In this video, Krista King from integralCALC Academy discusses Tabular Integration.
Lecture 30 Play Video	Partial Fractions, Distinct Linear Factors (Example 3) In this video, Krista King from integralCALC Academy talks about Partial Fractions (Calculus example).
Lecture 31 Play Video	Partial Fractions, Repeated Linear Factors In this video, Krista King from integralCALC Academy talks about Partial Fractions and Repeated Linear Factors (Calculus problem example).
Lecture 32 Play Video	Partial Fractions, Distinct Quadratic Factors (Example 3) In this video, Krista King from integralCALC Academy shows how to use partial fractions to calculate the integral of a rational function, which is the quotient of two polynomials, that has distinct quadratic factors in its denominator. To use partial fractions, you'll set up your partial fractions decomposition and then use simultaneous equations to solve for constants, then take the integral of the simplified decomposition. You may need to separate your fractions into their own integrals, and use u-substitution, or the integration formula with the inverse tangent.
Lecture 33 Play Video	Partial Fractions, Repeated Quadratic Factors In this video, Krista King from integralCALC Academy talks about Partial Fractions and Repeated Quadratic Factors (Calculus problem example).
Lecture 34 Play Video	Partial Fractions, Rationalizing Substitution In this video, Krista King from integralCALC Academy shows how to use a rationalization substitution to convert a function into one which can be evaluated using partial fractions.
Lecture 35 Play Video	Trigonometric Integrals In this video, Krista King from integralCALC Academy talks about Trigonometric Integrals (Calculus example).
Lecture 36 Play Video	Trigonometric Integrals: sin^mcos^n and odd m In this video, Krista King from integralCALC Academy shows how to find the integral of the product of a higher order sine function and higher order cosine function. In this particular example, we'll talk about the method for finding the integral when sine is odd and cosine is even.
Lecture 37 Play Video	Trigonometric Integrals: sin^mcos^n and odd n In this video, Krista King from integralCALC Academy shows how to find the integral of the product of a higher order sine function and higher order cosine function. In this particular example, we'll talk about the method for finding the integral when sine is even and cosine is odd.
Lecture 38 Play Video	Trigonometric Integrals: sin^mcos^n, m and n even In this video, Krista King from integralCALC Academy shows how to find the integral of the product of a higher order sine function and higher order cosine function. In this particular example, we'll talk about the method for finding the integral when sine and cosine are even
Lecture 39 Play Video	Integrals of Trigonometric Functions: tan^msec^n and odd m In this video, Krista King from integralCALC Academy shows how to evaluate an integral of the form (tan^m)(sec^n), where m, the degree of the tangent function, is odd.
Lecture 40 Play Video	Integrals of Trigonometric Functions: tan^msec^n and even n In this video, Krista King from integralCALC Academy shows how to evaluate an integral of the form (tan^m)(sec^n), where n, the degree of the secant function, is even.
Lecture 41 Play Video	Integrals of Trigonometric Functions: sin(mx)cos(nx) In this video, Krista King from integralCALC Academy shows how to evaluate an integral of the form sin(mx)cos(nx).
Lecture 42 Play Video	Integrals of Trigonometric Functions: sin(mx)sin(nx) In this video, Krista King from integralCALC Academy shows how to evaluate an integral of the form sin(mx)sin(nx).
Lecture 43 Play Video	Integrals of Trigonometric Functions: cos(mx)cos(nx) In this video, Krista King from integralCALC Academy shows how to evaluate an integral of the form cos(mx)cos(nx).
Lecture 44 Play Video	Integrals of Hyperbolic Functions In this video, Krista King from integralCALC Academy talks about Integrals of Hyperbolic Functions (Calculus problem example).
Lecture 45 Play Video	Integrals of Inverse Hyperbolic Functions In this video, Krista King from integralCALC Academy talks about Integrals of Inverse Hyperbolic Functions (Calculus problem example).
Lecture 46 Play Video	Setting Up Trigonometric Substitution In this video, Krista King from integralCALC Academy talks about Trigonometric Substitution.
Lecture 47 Play Video	Trigonometric Substitution with Secant In this video, Krista King from integralCALC Academy shows how to use trigonometric substitution with a secant substitution to evaluate an integral.
Lecture 48 Play Video	Trigonometric Substitution with Tangent In this video, Krista King from integralCALC Academy shows how to use trigonometric substitution with a tangent substitution to evaluate an integral.
Lecture 49 Play Video	Trigonometric Substitution with Sine In this video, Krista King from integralCALC Academy shows how to use trigonometric substitution with a sine substitution to evaluate an integral.
Lecture 50 Play Video	Improper Integral (Part I) In this video, Krista King from integralCALC Academy talks about Improper Integrals (Calculus example).
Lecture 51 Play Video	Improper Integral (Part II) In this video, Krista King from integralCALC Academy talks about Improper Integrals (Calculus example).
Lecture 52 Play Video	Integrals Using Reduction Formulas In this video, Krista King from integralCALC Academy shows how to use a reduction formula to evaluate an integral.
Lecture 53 Play Video	Average Value of the Function In this video, Krista King from integralCALC Academy shows how to find the average value of a function.
Lecture 54 Play Video	Area Between Curves - dx In this video, Krista King from integralCALC Academy shows how to find the area bounded by two curves. In this example, the curves are defined for y in terms of x, and you'll integrate with respect to x.
Lecture 55 Play Video	Area Between Curves - dy In this video, Krista King from integralCALC Academy shows how to find the area bounded by two curves. In this example, the curves are defined for x in terms of y, and you'll integrate with respect to y.
Lecture 56 Play Video	Area Between Curves: Sketching In this video, Krista King from integralCALC Academy shows how to sketch the area of the region bounded by the given curves, how to decide whether to integrate with respect to x or y, how to draw a typical approximating rectangle and label its height and width, and then how to find the area of the region, aka the area bounded by the given curves, aka the area between curves.
Lecture 57 Play Video	Arc Length x=g(y) In this video, Krista King from integralCALC Academy shows how to find the arc length of a curve on a given interval when the function is defined for x in terms of y, as x=g(y). Use the arc length formula.
Lecture 58 Play Video	Surface Area of Revolution In this video, Krista King from integralCALC Academy shows how to calculate the surface of revolution when revolving around the y-axis.
Lecture 59 Play Video	Surface of Revolution In this video, Krista King from integralCALC Academy talks about Surface of Revolution (Calculus example).
Lecture 60 Play Video	Volume of Rotation: Disk Method about the y-xis In this video, Krista King from integralCALC Academy shows how to use the disk and washer method to find the volume obtained by rotating the region bounded by the given curves about the given axis. In this particular problem, we'll use an approximating disk to find the volume of rotation about the y-axis.
Lecture 61 Play Video	Volume of Rotation: Disk Method about the x-axis In this video, Krista King from integralCALC Academy shows how to use the disk and washer method to find the volume obtained by rotating the region bounded by the given curves about the given axis. In this particular problem, we'll use an approximating disk to find the volume of rotation about the x-axis.
Lecture 62 Play Video	Volume of Rotation: Washer Method about y-axis In this video, Krista King from integralCALC Academy shows how to find the volume of rotation around a line defined for x in terms of y. Volume of rotation problems are essentially area between curves problems but with a slightly different formula that accounts for the 3D component.
Lecture 63 Play Video	Volume of Rotation: Washer Method about x-axis In this video, Krista King from integralCALC Academy shows how to find the volume of rotation around a line defined for y in terms of x. Volume of rotation problems are essentially area between curves problems but with a slightly different formula that accounts for the 3D component.
Lecture 64 Play Video	Volume of Rotation: Cylindrical Shells about the y-axis In this video, Krista King from integralCALC Academy shows how to use the cylindrical shells method to find the volume obtained by rotating the region bounded by given curves around a given axis. In this particular problem, we'll rotate about the line defined as x=a.
Lecture 65 Play Video	Volume of Rotation: Cylindrical Shells about the x-axis In this video, Krista King from integralCALC Academy shows how to use the cylindrical shells method to find the volume obtained by rotating the region bounded by given curves around a given axis. In this particular problem, we'll rotate about the line defined as y=a.
Lecture 66 Play Video	Mean Value Theorem for Integrals In this video, Krista King from integralCALC Academy shows how to use the Mean Value Theorem for integrals to prove that the function assumes the same value as its average on a given interval.
Lecture 67 Play Video	Work In this video, Krista King from integralCALC Academy shows how to find the work required to use a rope to hoist a weight from the ground up to the top of a building.
Lecture 68 Play Video	Work Done on Elastic Springs In this video, Krista King from integralCALC Academy talks about Work Done on Elastic Springs (Calculus problem example).
Lecture 69 Play Video	Work Done by a Variable Force In this video, Krista King from integralCALC Academy discusses Work Done by a Variable Force (Calculus problem example).
Lecture 70 Play Video	Center of Mass of the System In this video, Krista King from integralCALC Academy shows how to find the center of mass of the system given three masses and their locations in coordinate points.
Lecture 71 Play Video	Moments of the System In this video, Krista King from integralCALC Academy shows how to find the moments of a system given point masses and their coordinates.
Lecture 72 Play Video	Hydrostatic Force In this video, Krista King from integralCALC Academy shows how to find the hydrostatic force on the bottom and on one end of a tank filled with water.
Lecture 73 Play Video	Hydrostatic Pressure In this video, Krista King from integralCALC Academy shows how to find the hydrostatic pressure on the bottom of a tank filled with water.
Lecture 74 Play Video	Vertical Motion (Integration) In this video, Krista King from integralCALC Academy explains a vertical motion (Calculus problem example).
Lecture 75 Play Video	Rectilinear Motion In this video, Krista King from integralCALC Academy explains a rectilinear motion (Calculus problem example).
Lecture 76 Play Video	Centroids of Plane Regions In this video, Krista King from integralCALC Academy talks about Centroids of Plane Regions (Calculus problem example).
Lecture 77 Play Video	Area of the Triangle with the Given Vertices In this video, Krista King from integralCALC Academy shows how to find the area of a triangle with the given vertices. Once you find the equations of the sides of the triangle, this is essentially an area between curves problem.
Lecture 78 Play Video	Present and Future Value In this video, Krista King from integralCALC Academy talks about Present and Future Value (Calculus example).
Lecture 79 Play Video	Consumer and Producer Surplus In this video, Krista King from integralCALC Academy talks about Consumer and Producer Surplus (Calculus problem example).
Lecture 80 Play Video	Probability Density Functions In this video, Krista King from integralCALC Academy shows how to identify a probability density function and find the probability that x falls on a particular interval.
Lecture 81 Play Video	Cardiac Output In this video, Krista King from integralCALC Academy shows how to use a formula for flow or flux to find cardiac output with the dye injection method, given the amount of dye injected, and a function that models the amount of dye remaining in the atrium at intervals (in seconds) after the injection.
Lecture 82 Play Video	Poiseuille's Law In this video, Krista King from integralCALC Academy shows how to use Poiseuille's law to find the flow or flux of a human artery, given the formula for the law, the pressure difference between each end of the artery, the radius of the artery, the viscosity of the blood, and the length of the artery.
Lecture 83 Play Video	Theorem of Pappus In this video, Krista King from integralCALC Academy shows how to use the Theorem of Pappus to find the volume of a solid, in this particular case, a right circular cone. Theorem of Pappus tells us that volume is equal to area of the plane region, times the distance traveled by the centroid of the same plane region, if the plane region is revolved around the x-axis.
Lecture 84 Play Video	Analytic Geometry: Graph of a Single Point or of No Points In this video, Krista King from integralCALC Academy discusses Analytic Geometry and graphing of a single point or of no points (Calculus problem example).
Lecture 85 Play Video	Analytic Geometry: Set of Points Equally Distant from Two Points In this video, Krista King from integralCALC Academy discusses Analytic Geometry and the set of points equally distant from two points (Calculus problem example).
Lecture 86 Play Video	Analytic Geometry: Set of Points Unequally Distant from Two Points In this video, Krista King from integralCALC Academy discusses Analytic Geometry and the set of points unequally distant from two points (Calculus problem example).
Lecture 87 Play Video	Eccentricity and Directrix of the Conic Section In this video, Krista King from integralCALC Academy shows how to use the polar equation of a conic section to identify the conic as a parabola, an ellipse, or a hyperbola, find eccentricity and the equation of the directrix, and the sketch the conic.
Lecture 88 Play Video	Parabolas: Vertex, Axis, Focus, and Directrix In this video, Krista King from integralCALC Academy discusses parabolas, including vertex, axis, focus, and directrix (Calculus problem example).
Lecture 89 Play Video	Equation of a Parabola (Conic Section) In this video, Krista King from integralCALC Academy shows how to find the equation of a parabolic conic section with a given vertex, vertical axis, and passing through a given point.
Lecture 90 Play Video	Polar Equation of the Parabola (Conic Section) In this video, Krista King from integralCALC Academy shows how to find the polar equation of the parabolic conic section with focus at the origin, given only its vertex.
Lecture 91 Play Video	Vertex Axis Focus Directrix of an Ellipse In this video, Krista King from integralCALC Academy shows how to find the vertex, axis, focus, center and directrix of an ellipse, and then sketch and label the graph of the ellipse.
Lecture 92 Play Video	Equation of an Ellipse (Conic Section) In this video, Krista King from integralCALC Academy shows how to find the equation of an elliptical conic section given its foci and vertices.
Lecture 93 Play Video	Polar Equation of the Ellipse (Conic Section) In this video, Krista King from integralCALC Academy shows how to find the polar equation of an elliptical conic section with focus at the origin, given only its eccentricity and the equation of its directrix.
Lecture 94 Play Video	Vertex Axis Focus Directrix Asymptotes of a Hyperbola In this video, Krista King from integralCALC Academy shows how to find the vertex, axis, focus, center and directrix of a hyperbola, and then sketch and label the graph of the hyperbola.
Lecture 95 Play Video	Equation of a Hyperbola (Conic Section) In this video, Krista King from integralCALC Academy shows how to find the equation of a hyperbolic conic section given its foci and vertices.
Lecture 96 Play Video	Polar Equation of the Hyperbola (Conic Section) In this video, Krista King from integralCALC Academy shows how to find the polar equation of a hyperbola with focus at the origin, given only its eccentricity and the equation of its directrix.
Lecture 97 Play Video	Eliminating the Parameter In this video, Krista King from integralCALC Academy shows how to eliminate the parameter (Calculus problem example).
Lecture 98 Play Video	Derivative of a Parametric Curve In this video, Krista King from integralCALC Academy shows how to find the derivative of the parametric curve, which is defined by two functions, one function of y in terms of t, and one function of x in terms of t.
Lecture 99 Play Video	Second Derivative of a Parametric Curve In this video, Krista King from integralCALC Academy shows how to calculate the second derivative of a parametric curve.
Lecture 100 Play Video	Tangent Line to the Parametric Curve In this video, Krista King from integralCALC Academy shows how to calculate the derivative of a parametric curve and find the equation of the tangent line to the parametric curve at a given point t.
Lecture 101 Play Video	Sketch the Parametric Curve by Plotting Points In this video, Krista King from integralCALC Academy shows how to sketch the parametric curve by plotting points. You'll need to identify values of t, plug them into your parametric equations for x and y, and thereby find x and y values which will become the coordinate points that you can plot in an x-y coordinate plane.
Lecture 102 Play Video	Area Under the Parametric Curve In this video, Krista King from integralCALC Academy shows how to find the area under the parametric curve and above the x-axis.
Lecture 103 Play Video	Parametric Area Under One Arc or Loop In this video, Krista King from integralCALC Academy shows how to find the area under one arc or loop of a parametric curve.
Lecture 104 Play Video	Parametric Curve: Surface Area of Revolution In this video, Krista King from integralCALC Academy discusses parametric curves, particularly surface area of revolution (Calculus problem example).
Lecture 105 Play Video	Surface Area of Revolution of a Parametric Curve Rotated About the y-axis In this video, Krista King from integralCALC Academy shows how to find the surface area of revolution of a parametric curve rotated about the y-axis.
Lecture 106 Play Video	Parametric Arc Length In this video, Krista King from integralCALC Academy shows how to find the arc length of a parametric curve.
Lecture 107 Play Video	Parametric Arc Length and the distance Traveled by the Particle In this video, Krista King from integralCALC Academy shows how to find the arc length of a parametric curve, calculate geometrically the distance traveled by a particle, and then compare the two values.
Lecture 108 Play Video	Volume of Revolution of a Parametric Curve In this video, Krista King from integralCALC Academy talks about the volume of revolution of a parametric curve (Calculus problem example).
Lecture 109 Play Video	Converting Polar Coordinates In this video, Krista King from integralCALC Academy shows how to convert polar coordinates (Calculus example).
Lecture 110 Play Video	Converting Rectangular Equations to Polar Equations In this video, Krista King from integralCALC Academy shows how to convert rectangular equations to polar equations.
Lecture 111 Play Video	Converting Polar Equations to Rectangular Equations In this video, Krista King from integralCALC Academy shows how to convert polar equations to rectangular equations.
Lecture 112 Play Video	Distance Between Two Polar Points In this video, Krista King from integralCALC Academy shows how to find the distance between two polar coordinate points.
Lecture 113 Play Video	Sketching Polar Curves from Cartesian Curves In this video, Krista King from integralCALC Academy shows how to sketch a polar curve from the picture of a cartesian curve.
Lecture 114 Play Video	Sketching Polar Curves: 2 Examples In this video, Krista King from integralCALC Academy gives a Calculus example for sketching polar curves.
Lecture 115 Play Video	Tangent Line to the Polar Curve In this video, Krista King from integralCALC Academy shows how to find the tangent line to the polar curve.
Lecture 116 Play Video	Vertical and Horizontal Tangent Lines to the Polar Curve In this video, Krista King from integralCALC Academy shows how to find the points on the polar curve where the tangent line to the curve is either vertical or horizontal.
Lecture 117 Play Video	Polar Area In this video, Krista King from integralCALC Academy talks about polar area (Calculus example).
Lecture 118 Play Video	Polar Area Bounded by One Loop In this video, Krista King from integralCALC Academy talks about polar area bounded by one loop (Calculus problem example).
Lecture 119 Play Video	Points of Intersection of Two Polar Curves In this video, Krista King from integralCALC Academy shows how to find the points of intersection of two polar curves.
Lecture 120 Play Video	Area Between Polar Curves In this video, Krista King from integralCALC Academy talks about the area between polar curves (Calculus problem example).
Lecture 121 Play Video	Polar Area Inside Both Curves In this video, Krista King from integralCALC Academy shows how to find the area inside two polar curves.
Lecture 122 Play Video	Arc Length of a Polar Curve In this video, Krista King from integralCALC Academy discusses arc length of a polar curve (Calculus problem example).
Lecture 123 Play Video	Polar Parametric Curve: Surface Area of Revolution In this video, Krista King from integralCALC Academy talks about polar parametric curves, particularly surface area of revolution (Calculus problem example).
Lecture 124 Play Video	Polar Parametric Curve: Arc Length In this video, Krista King from integralCALC Academy talks about polar parametric curve, particularly arc length (Calculus problem example).
Lecture 125 Play Video	Listing the First Terms of the Sequence In this video, Krista King from integralCALC Academy shows how to use the first term and an equation for the nth plus one term to list the first several terms in the sequence.
Lecture 126 Play Video	Calculating the First Terms of the Sequence In this video, Krista King from integralCALC Academy shows how to use a formula for the general term of the sequence, a_n, to calculate the first several terms of the sequence. Then use the values of the first several terms to draw a conclusion about the limit of the sequence as n approaches infinity.
Lecture 127 Play Video	Finding a Formula for the General Term of the Sequence (a_n) In this video, Krista King from integralCALC Academy shows how to use a list of the first several terms of the sequence to find a formula for the general term of the sequence, a_n
Lecture 128 Play Video	Does the Sequence Converge or Diverge? In this video, Krista King from integralCALC Academy shows how to determine whether the sequence converges or diverges. In this problem I show you how to find the limit of the sequence, if it exists, and then use the existence or nonexistence of the limit to draw a conclusion about the convergence of the sequence. Alternately, I show you how to use Squeeze Theorem to first draw a conclusion about the convergence of the sequence, and then to use the result to find the limit of the sequence, if it converges.
Lecture 129 Play Video	Finding the Limit of a Convergent Sequence In this video, Krista King from integralCALC Academy shows how to find the limit of a convergent sequence. Since we've been told that the sequence converges, we know automatically by the definition that the limit exists.
Lecture 130 Play Video	Increasing, Decreasing and not Monotonic Sequences In this video, Krista King from integralCALC Academy shows how to determine whether a sequence is increasing, decreasing, or not monotonic. We'll also talk about whether we can say that the sequence is bounded above and/or whether it's bounded below.
Lecture 131 Play Video	Bounded Sequences In this video, Krista King from integralCALC Academy shows how to determine whether or not a sequence is bounded. First you'll need to determine whether or not the sequence is monotonic, and if it is, whether or not it is increasing or decreasing. If the sequence is monotonic, then you can use your conclusion about whether it is increasing or decreasing to tell you whether it is bounded above and/or bounded below. You'll also need to take the limit of the sequence as n approaches infinity.
Lecture 132 Play Video	Calculating the First Terms in a Series of Partial Sums In this video, Krista King from integralCALC Academy shows how to calculate the first terms of a series of partial sums. You'll do this by plugging in values for n to get the values of the regular series, then you'll add the values of the regular series together to the values in the series of partial sums.
Lecture 133 Play Video	Sum of the Series of Partial Sums In this video, Krista King from integralCALC Academy shows how to find the sum of the series using its corresponding series of partial sums. Understand the difference between a series and a series of partial sums, and then use the fact that the sum of an infinite series is equal to the limit as n goes to infinity of the series of partial sums to the find the sum of the infinite series.
Lecture 134 Play Video	Repeating Decimal Expressed as a Ratio of Integers In this video, Krista King from integralCALC Academy shows how to express the repeating decimal as a ratio of integers. You'll change the repeating part of the decimal into a geometric series, then find the sum of the geometric series and use it to find a ratio of integers (fraction of whole numbers) that expresses the repeating decimal.
Lecture 135 Play Video	nth Term Test, Divergence Test, and the Zero Test In this video, Krista King from integralCALC Academy shows how to use the nth term test, aka divergence test, aka zero test, as a quick way to see whether a series diverges. Remember that this test tells you nothing about convergence. If the limit of the series is not equal to zero, then you can safely conclude that the series diverges, but you can't draw any additional conclusions. If the limit to the series is equal to zero, then the divergence test is inconclusive, and you have to use another test to determine convergence/divergence of the series.
Lecture 136 Play Video	Convergence of a Geometric Series In this video, Krista King from integralCALC Academy shows how to determine whether a geometric series converges or diverges and if it converges, how to find its sum.
Lecture 137 Play Video	Convergence and Sum of a Geometric Series (Example 1) In this video, Krista King from integralCALC Academy talks about Infinite Series (Calculus example).
Lecture 138 Play Video	Values for Which the Geometric Series Converges In this video, Krista King from integralCALC Academy shows how to find the values for which the geometric series converges.
Lecture 139 Play Video	Convergence of a Telescoping Series In this video, Krista King from integralCALC Academy shows how to determine whether a telescoping series converges or diverges and if it converges, how to find its sum.
Lecture 140 Play Video	Sum of Telescoping Series In this video, Krista King from integralCALC Academy talks about sum of telescoping series (Calculus problem example).
Lecture 141 Play Video	p-Series Test for Convergence In this video, Krista King from integralCALC Academy shows how to use the p-series test to determine whether or not a series converges
Lecture 142 Play Video	Integral Test for Convergence In this video, Krista King from integralCALC Academy talks about integral test for convergence (Calculus problem example).
Lecture 143 Play Video	Comparison Test In this video, Krista King from integralCALC Academy talks about Comparison Test (Calculus problem example).
Lecture 144 Play Video	Limit Comparison Test In this video, Krista King from integralCALC Academy talks about the limit comparison test (Calculus problem example).
Lecture 145 Play Video	Estimating Error/Remainder of a Series In this video, Krista King from integralCALC Academy shows how to estimate the error of a series using the first ten terms of the series and a comparison series.
Lecture 146 Play Video	Alternating Series Test In this video, Krista King from integralCALC Academy talks about the Alternating Series Test (Calculus problem example).
Lecture 147 Play Video	Alternating Series Estimation Theorem In this video, Krista King from integralCALC Academy shows how to use the alternating series estimation theorem to estimate the sum of a series and find the remainder term, which is the difference between the estimation and the exact sum of the series.
Lecture 148 Play Video	Ratio Test In this video, Krista King from integralCALC Academy talks about the Ratio Test (Calculus problem example).
Lecture 149 Play Video	Ratio Test with Factorials In this video, Krista King from integralCALC Academy talks about the Ratio Test with Factorials (Calculus problem example).
Lecture 150 Play Video	Root Test In this video, Krista King from integralCALC Academy talks about the Root Test (Calculus problem example).
Lecture 151 Play Video	Absolute and Conditional Convergence In this video, Krista King from integralCALC Academy shows how to determine whether the series converges absolutely or conditionally using the ratio and root tests.
Lecture 152 Play Video	Difference Between Limit and Sum of the Series In this video, Krista King from integralCALC Academy talks about the difference between limit and sum of the series (Calculus problem example).
Lecture 153 Play Video	Radius of Convergence In this video, Krista King from integralCALC Academy shows how to find the radius of convergence of a series using the ratio test.
Lecture 154 Play Video	Interval of Convergence In this video, Krista King from integralCALC Academy talks about the Interval of Convergence (Calculus example).
Lecture 155 Play Video	Power Series Representation, Radius and Interval of Convergence In this video, Krista King from integralCALC Academy shows how to represent a function as a power series and then find the associated radius of convergence and interval of convergence of the power series.
Lecture 156 Play Video	Power Series Differentiation In this video, Krista King from integralCALC Academy shows how to differentiate a power series in order to find the power series representation of a function and its associated radius of convergence.
Lecture 157 Play Video	Expressing the Integral as a Power Series In this video, Krista King from integralCALC Academy shows how to use power series to evaluate an indefinite integral. Then find the associated radius of convergence of the power series.
Lecture 158 Play Video	Using Power Series to Estimate a Definite Integral In this video, Krista King from integralCALC Academy shows how to use power series to estimate a definite integral.
Lecture 159 Play Video	Taylor Polynomial (Part I) In this video, Krista King from integralCALC Academy talks about Taylor Polynomials (Calculus example).
Lecture 160 Play Video	Taylor Polynomial (Part II) In this video, Krista King from integralCALC Academy talks about Taylor Polynomials (Calculus example).
Lecture 161 Play Video	Finding Radius of Convergence of a Taylor Series In this video, Krista King from integralCALC Academy shows how to find the radius of convergence of a Taylor series. First create a table and use it to write out the first several terms of the Taylor series. Then find a representation for the a_n-th and express the series as an infinite sum. Then use Ratio Test to find the radius of convergence of the Taylor series.
Lecture 162 Play Video	Taylor's Inequality In this video, Krista King from integralCALC Academy shows how to use Taylor's inequality to show that the sum of a Maclaurin series is representative of the series for all values of x.
Lecture 163 Play Video	Maclaurin Series In this video, Krista King from integralCALC Academy talks about the Maclaurin Series (Calculus problem example).
Lecture 164 Play Video	Sum of the Maclaurin Series In this video, Krista King from integralCALC Academy shows how to find the sum of the maclaurin series, which is the taylor series centered at 0, or with a=0. You can easily find the sum of the series if you can compare the given series to a well known maclaurin series.
Lecture 165 Play Video	Maclaurin Series Radius of Convergence In this video, Krista King from integralCALC Academy shows how to use Ratio Test to determine the convergence of a maclaurin series, then find the radius of convergence of the maclaurin series by comparing it to a well known maclaurin series.
Lecture 166 Play Video	Power Series Division In this video, Krista King from integralCALC Academy shows how to use power series division to find the first three non-zero terms of the maclaurin series.
Lecture 167 Play Video	Power Series Multiplication In this video, Krista King from integralCALC Academy shows how to use power series multiplication to find the first three non-zero terms of the maclaurin series.
Lecture 168 Play Video	Binomial Series In this video, Krista King from integralCALC Academy shows how to use the binomial series to expand the function as a power series. Then state the radius of convergence of the power series.
Lecture 169 Play Video	Expressing an Indefinite Integral as an Infinite Series In this video, Krista King from integralCALC Academy shows how to express an indefinite integral as the sum of an infinite series.
Lecture 170 Play Video	Using Maclaurin Series to Estimate an Indefinite Integral In this video, Krista King from integralCALC Academy shows how to use Maclaurin Series to estimate the value of an indefinite integral.
Lecture 171 Play Video	Maclaurin Series to Estimate a Definite Integral In this video, Krista King from integralCALC Academy shows how to use a Maclaurin series to estimate a definite integral
Lecture 172 Play Video	Maclaurin Series to Evaluate a Limit In this video, Krista King from integralCALC Academy shows how to use a Maclaurin series to evaluate a limit. We'll find the Maclaurin series for sinx, then substitute the first several terms of the series into our function so that we're taking the limit of an entirely polynomial function.
Lecture 173 Play Video	Improper Integrals (Case 2) In this video, Krista King from integralCALC Academy shows how to integrate an improper integral with limits of integration (-infinity,b].
Lecture 174 Play Video	Partial Fractions: Two Ways to Find the Constants In this video, Krista King from integralCALC Academy shows two different methods for finding the constants in a partial fractions decomposition. The first, and more complicated way, is to set up a system of simultaneous linear equations, and then use substitution or elimination to solve to the system. The second, and simpler way, is to find the value that will zero out one constant so that you can solve for the other.The simpler way only works in specific instances, which is why I prefer to stick to the first method, the system of linear equations, which is guaranteed to always work.
Lecture 175 Play Video	Improper Integrals (Case 3) In this video, Krista King from integralCALC Academy shows how to evaluate improper integrals of case type 3, which are improper integrals over the interval (-infinity,infinity). We'll pick a value c inside the interval and split the interval at c, turning the type 3 improper integral into the sum of a type 1 and type 2 improper integral. Then we'll change each of those into definite integrals with limits.
Lecture 176 Play Video	Integrating with Partial Fractions: How to Factor Difficult Denominators In this video, Krista King from integralCALC Academy shows how to factor a complicated denominator in order to get a function ready for integration with partial fractions. Sometimes we'll be able to pull out the greatest common factor (GCF), and sometimes the denominator will be the sum of cubes or the difference of cubes. Or sometimes we might be able to use substitution or grouping to factor the denominator. The example we work through will be factorable by grouping, and then we'll be able to use partial fractions to integrate the function.