Introduction
The derivative tells us the rate of change of a function whose values we know. The definite integral tells us the value of a function whose rate of change and initial conditions are known.
**Part A: Definition of the Definite Integral and First Fundamental Theorem**
- Session 43: Definite Integrals
- Session 44: Adding Areas of Rectangles
- Session 45: Some Easy Integrals
- Session 46: Riemann Sums
- Session 47: Introduction of the Fundamental Theorem of Calculus
- Session 48: The Fundamental Theorem of Calculus
- Session 49: Applications of the Fundamental Theorem of Calculus
- Session 50: Combining the Fundamental Theorem and the Mean Value Theorem
- Problem Set 6
**Part B: Second Fundamental Theorem, Areas, Volumes**
- Session 51: The Second Fundamental Theorem of Calculus
- Session 52: Proving the Fundamental Theorem of Calculus
- Session 53: New Functions From Old
- Session 54: The Second Fundamental Theorem and ln(x)
- Session 55: Creating New Functions Using the Second Fundamental Theorem
- Session 56: Geometric Interpretation of Definite Integrals
- Session 57: How to Calculate Volumes
- Session 58: Volume of a Sphere, Revolving About x-axis
- Session 59: Volume of a Parabaloid, Revolving About y-axis
- Problem Set 7
**Part C: Average Value, Probability and Numerical Integration**