3. The Definite Integral and its Applications

Part B: Second Fundamental Theorem, Areas, Volumes

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The Second Fundamental Theorem of Calculus describes how integration is the opposite of differentiation. It allows us to understand functions defined in terms of definite integrals, some of which are impossible to describe using more elementary methods. This part of the course also covers the use of integration to calculate volumes of solids.

» 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

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