# Calculus II

### Course Description

In this course, Krista King from the integralCALC Academy covers a range of topics in Calculus II, including Integrals, Applications of Integrals, Polar & Parametric of Sequences & Series.

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### Video Lectures & Study Materials

Visit the official course website for more study materials: https://www.integralcalc.com

# Lecture Play Lecture
1 Area Under the Curve (Example 1) (0012:53) Play Video
2 Area Under the Graph vs. Area Enclosed by the Graph (004:55) Play Video
3 Summation Notation: Finding the Sum (003:55) Play Video
4 Summation Notation: Expanding (002:26) Play Video
5 Summation Notation: Collapsing (004:12) Play Video
6 Riemann Sums Right Endpoints (008:12) Play Video
7 Riemann Sums Midpoints (008:51) Play Video
8 Trapezoidal Rule (0014:52) Play Video
9 Simpson's Approximation (009:41) Play Video
10 Definite Integral (005:02) Play Video
11 Definite Integral of an Even Function (005:24) Play Video
12 Definite Integral of an Odd Function (008:02) Play Video
13 Fundamental Theorem of Calculus (Part I) (009:36) Play Video
14 Fundamental Theorem of Calculus (Part II) (004:52) Play Video
15 Indefinite Integrals (002:36) Play Video
16 Properties of integrals (005:58) Play Video
17 Find f(x) Given f''(x), its Second Derivative (005:06) Play Video
18 Find f Given f'' and Initial Conditions (008:48) Play Video
19 Find f(x) Given f'''(x), its Third Derivative (007:43) Play Video
20 Integral of a Quadratic Function (0014:25) Play Video
21 Initial Value Problem (002:51) Play Video
22 U-Substitution (004:17) Play Video
23 U-Substitution in Definite Integrals (009:21) Play Video
24 U-Substitution with Integration by Parts (009:13) Play Video
25 Integration by Parts (009:09) Play Video
26 Integration by Parts Two Times (0014:00) Play Video
27 Integration by Parts Three Times (0010:55) Play Video
28 Integration by Parts to Prove the Reduction Formula (007:31) Play Video
29 Tabular Integration (008:54) Play Video
30 Partial Fractions, Distinct Linear Factors (Example 3) (0011:44) Play Video
31 Partial Fractions, Repeated Linear Factors (0012:43) Play Video
32 Partial Fractions, Distinct Quadratic Factors (Example 3) (0016:26) Play Video
33 Partial Fractions, Repeated Quadratic Factors (0017:25) Play Video
34 Partial Fractions, Rationalizing Substitution (0012:48) Play Video
35 Trigonometric Integrals (004:06) Play Video
36 Trigonometric Integrals: sin^mcos^n and odd m (0010:17) Play Video
37 Trigonometric Integrals: sin^mcos^n and odd n (0011:23) Play Video
38 Trigonometric Integrals: sin^mcos^n, m and n even (007:37) Play Video
39 Integrals of Trigonometric Functions: tan^msec^n and odd m (005:43) Play Video
40 Integrals of Trigonometric Functions: tan^msec^n and even n (005:50) Play Video
41 Integrals of Trigonometric Functions: sin(mx)cos(nx) (003:58) Play Video
42 Integrals of Trigonometric Functions: sin(mx)sin(nx) (004:33) Play Video
43 Integrals of Trigonometric Functions: cos(mx)cos(nx) (004:41) Play Video
44 Integrals of Hyperbolic Functions (003:41) Play Video
45 Integrals of Inverse Hyperbolic Functions (004:41) Play Video
46 Setting Up Trigonometric Substitution (008:55) Play Video
47 Trigonometric Substitution with Secant (0013:58) Play Video
48 Trigonometric Substitution with Tangent (0017:32) Play Video
49 Trigonometric Substitution with Sine (0019:04) Play Video
50 Improper Integral (Part I) (006:53) Play Video
51 Improper Integral (Part II) (004:23) Play Video
52 Integrals Using Reduction Formulas (007:51) Play Video
53 Average Value of the Function (006:19) Play Video
54 Area Between Curves - dx (0010:32) Play Video
55 Area Between Curves - dy (007:21) Play Video
56 Area Between Curves: Sketching (0011:01) Play Video
57 Arc Length x=g(y) (0011:27) Play Video
58 Surface Area of Revolution (0011:39) Play Video
59 Surface of Revolution (003:12) Play Video
60 Volume of Rotation: Disk Method about the y-xis (0010:05) Play Video
61 Volume of Rotation: Disk Method about the x-axis (009:04) Play Video
62 Volume of Rotation: Washer Method about y-axis (0010:39) Play Video
63 Volume of Rotation: Washer Method about x-axis (0011:11) Play Video
64 Volume of Rotation: Cylindrical Shells about the y-axis (0012:39) Play Video
65 Volume of Rotation: Cylindrical Shells about the x-axis (0011:26) Play Video
66 Mean Value Theorem for Integrals (004:16) Play Video
67 Work (007:58) Play Video
68 Work Done on Elastic Springs (006:51) Play Video
69 Work Done by a Variable Force (005:53) Play Video
70 Center of Mass of the System (003:34) Play Video
71 Moments of the System (004:43) Play Video
72 Hydrostatic Force (0010:38) Play Video
73 Hydrostatic Pressure (003:12) Play Video
74 Vertical Motion (Integration) (0011:26) Play Video
75 Rectilinear Motion (007:06) Play Video
76 Centroids of Plane Regions (008:50) Play Video
77 Area of the Triangle with the Given Vertices (0011:54) Play Video
78 Present and Future Value (002:43) Play Video
79 Consumer and Producer Surplus (007:35) Play Video
80 Probability Density Functions (007:04) Play Video
81 Cardiac Output (008:47) Play Video
82 Poiseuille's Law (002:44) Play Video
83 Theorem of Pappus (0012:42) Play Video
84 Analytic Geometry: Graph of a Single Point or of No Points (005:43) Play Video
85 Analytic Geometry: Set of Points Equally Distant from Two Points (005:46) Play Video
86 Analytic Geometry: Set of Points Unequally Distant from Two Points (0012:15) Play Video
87 Eccentricity and Directrix of the Conic Section (009:50) Play Video
88 Parabolas: Vertex, Axis, Focus, and Directrix (0010:08) Play Video
89 Equation of a Parabola (Conic Section) (004:10) Play Video
90 Polar Equation of the Parabola (Conic Section) (003:46) Play Video
91 Vertex Axis Focus Directrix of an Ellipse (0013:48) Play Video
92 Equation of an Ellipse (Conic Section) (005:56) Play Video
93 Polar Equation of the Ellipse (Conic Section) (004:20) Play Video
94 Vertex Axis Focus Directrix Asymptotes of a Hyperbola (0015:16) Play Video
95 Equation of a Hyperbola (Conic Section) (007:11) Play Video
96 Polar Equation of the Hyperbola (Conic Section) (003:36) Play Video
97 Eliminating the Parameter (006:06) Play Video
98 Derivative of a Parametric Curve (003:17) Play Video
99 Second Derivative of a Parametric Curve (004:06) Play Video
100 Tangent Line to the Parametric Curve (009:14) Play Video
101 Sketch the Parametric Curve by Plotting Points (005:55) Play Video
102 Area Under the Parametric Curve (0014:56) Play Video
103 Parametric Area Under One Arc or Loop (007:11) Play Video
104 Parametric Curve: Surface Area of Revolution (0010:35) Play Video
105 Surface Area of Revolution of a Parametric Curve Rotated About the y-axis (0012:37) Play Video
106 Parametric Arc Length (0016:41) Play Video
107 Parametric Arc Length and the distance Traveled by the Particle (0015:55) Play Video
108 Volume of Revolution of a Parametric Curve (009:55) Play Video
109 Converting Polar Coordinates (003:13) Play Video
110 Converting Rectangular Equations to Polar Equations (003:22) Play Video
111 Converting Polar Equations to Rectangular Equations (003:02) Play Video
112 Distance Between Two Polar Points (009:15) Play Video
113 Sketching Polar Curves from Cartesian Curves (006:29) Play Video
114 Sketching Polar Curves: 2 Examples (0017:51) Play Video
115 Tangent Line to the Polar Curve (0010:06) Play Video
116 Vertical and Horizontal Tangent Lines to the Polar Curve (0010:39) Play Video
117 Polar Area (0010:01) Play Video
118 Polar Area Bounded by One Loop (0012:01) Play Video
119 Points of Intersection of Two Polar Curves (0013:15) Play Video
120 Area Between Polar Curves (0013:24) Play Video
121 Polar Area Inside Both Curves (0012:53) Play Video
122 Arc Length of a Polar Curve (007:59) Play Video
123 Polar Parametric Curve: Surface Area of Revolution (0010:37) Play Video
124 Polar Parametric Curve: Arc Length (007:07) Play Video
125 Listing the First Terms of the Sequence (003:01) Play Video
126 Calculating the First Terms of the Sequence (003:45) Play Video
127 Finding a Formula for the General Term of the Sequence (a_n) (006:36) Play Video
128 Does the Sequence Converge or Diverge? (007:55) Play Video
129 Finding the Limit of a Convergent Sequence (005:11) Play Video
130 Increasing, Decreasing and not Monotonic Sequences (0011:41) Play Video
131 Bounded Sequences (0012:21) Play Video
132 Calculating the First Terms in a Series of Partial Sums (005:10) Play Video
133 Sum of the Series of Partial Sums (004:51) Play Video
134 Repeating Decimal Expressed as a Ratio of Integers (009:28) Play Video
135 nth Term Test, Divergence Test, and the Zero Test (009:02) Play Video
136 Convergence of a Geometric Series (0011:48) Play Video
137 Convergence and Sum of a Geometric Series (Example 1) (0013:48) Play Video
138 Values for Which the Geometric Series Converges (006:01) Play Video
139 Convergence of a Telescoping Series (006:58) Play Video
140 Sum of Telescoping Series (0010:52) Play Video
141 p-Series Test for Convergence (003:10) Play Video
142 Integral Test for Convergence (006:59) Play Video
143 Comparison Test (0011:15) Play Video
144 Limit Comparison Test (008:51) Play Video
145 Estimating Error/Remainder of a Series (0012:06) Play Video
146 Alternating Series Test (0016:06) Play Video
147 Alternating Series Estimation Theorem (0013:15) Play Video
148 Ratio Test (007:25) Play Video
149 Ratio Test with Factorials (007:41) Play Video
150 Root Test (004:51) Play Video
151 Absolute and Conditional Convergence (0013:53) Play Video
152 Difference Between Limit and Sum of the Series (006:21) Play Video
153 Radius of Convergence (009:39) Play Video
154 Interval of Convergence (0014:00) Play Video
155 Power Series Representation, Radius and Interval of Convergence (0020:04) Play Video
156 Power Series Differentiation (0017:34) Play Video
157 Expressing the Integral as a Power Series (0012:34) Play Video
158 Using Power Series to Estimate a Definite Integral (0011:25) Play Video
159 Taylor Polynomial (Part I) (008:26) Play Video
160 Taylor Polynomial (Part II) (007:04) Play Video
161 Finding Radius of Convergence of a Taylor Series (0020:53) Play Video
162 Taylor's Inequality (008:57) Play Video
163 Maclaurin Series (005:08) Play Video
164 Sum of the Maclaurin Series (006:26) Play Video
165 Maclaurin Series Radius of Convergence (009:52) Play Video
166 Power Series Division (005:32) Play Video
167 Power Series Multiplication (007:10) Play Video
168 Binomial Series (0017:51) Play Video
169 Expressing an Indefinite Integral as an Infinite Series (008:09) Play Video
170 Using Maclaurin Series to Estimate an Indefinite Integral (009:47) Play Video
171 Maclaurin Series to Estimate a Definite Integral (007:27) Play Video
172 Maclaurin Series to Evaluate a Limit (005:48) Play Video
173 Improper Integrals (Case 2) (005:43) Play Video
174 Partial Fractions: Two Ways to Find the Constants (0019:33) Play Video
175 Improper Integrals (Case 3) (0012:24) Play Video
176 Integrating with Partial Fractions: How to Factor Difficult Denominators (0020:26) Play Video