# Calculus with Dr. Bob II: Basic Integration

### Course Description

In this second chapter of a series of calculus lessons, Dr. Bob covers integral calculus, including topics such as: Antiderivatives, Area, Definite Integrals, Fundamental Theorems of Calculus, Integration by Substitution, Trapezoid and Simpson's Rules. This series has 39 lessons, and it is a continuation of Part I: Limits and Derivatives.

Dr. Bob in Lesson 32, demonstrating Integration by Substitution of Definite Integrals
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### Video Lectures & Study Materials

# Lecture Play Lecture
1 Definition of Antiderivative Play Video
2 Antiderivative of a Polynomial Play Video
3 Antiderivative of (x-1)(x-2)/sqrt(x^3) Play Video
4 Basic Trig Antiderivatives Play Video
5 Antiderivative of tan^2(x) Play Video
6 Antiderivative of sin(x)/[1-sin^2(x)] Play Video
7 Visualizing an Antiderivative Play Video
8 Graphing f(x) from f'(x) Play Video
9 Antiderivative of a Piecewise-Defined Function Play Video
10 Solving Differential Equations Play Video
11 Equations of Motion Play Video
12 Overview of Rectangular Approximation of Area Play Video
13 Rectangular Approximation of Area Play Video
14 Overview of Summation Formulas Play Video
15 Limit Summation Formula Play Video
16 General Method for Integer Power Sum Formula Play Video
17 Riemann Sum with Signed Area Play Video
18 Limit Process for Area Play Video
19 Definition of Definite Integral Play Video
20 Definite Integral as Area 1 - Using the Graph Play Video
21 Definite Integral as Area 2 - Breaking Up the Region Play Video
22 Definite Integral as Area 3 - Area Below the x-axis Play Video
23 The First Fundamental Theorem of Calculus Play Video
24 Area Under a Curve 1 Play Video
25 Area Under a Curve 2 Play Video
26 The Mean Value Theorem for Integrals Play Video
27 Example of Mean Value Theorem for Integration Play Video
28 The Second Fundamental Theorem of Calculus Play Video
29 Example of 2nd Fundamental Theorem of Calculus 1 Play Video
30 Example of 2nd Fundamental Theorem of Calculus 2 Play Video
31 Integration By Substitution: Antiderivatives Play Video
32 Integration by Substitution: Definite Integrals Play Video
33 Example of Integration by Substitution 1: f(x) = (-x)/[(x+1)-sqrt(x+1)] Play Video
34 Example of Integration by Substitution 2: f(x) = x^5/(1-x^3)^3 Play Video
35 Example of Integration by Substitution 3: f(x) = x^2(1+x)^4 over [0,1] Play Video
36 Example of Integration by Substitution 4: f(x) = (2x+3)/sqrt(2x+1) Play Video
37 Example of Integration by Substitution 5: f(x) = sin(x)/cos^3(x) Play Video
38 Example of Trapezoid Rule with Error Bound Play Video
39 Example of Simpson's Rule with Error Bound Play Video

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