Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Calculus I
Topic: Antiderivatives
Subtopic: Theorems of Calculus (FTC, MVT for Integrals, AV)


This lesson includes theorems that form the guts of integral calculus. There are two Fundamental Theorems of Calculus (FTC) both connecting differentiation to integration. The Mean Value Theorem (MVT) for Integrals and its consequence the Average Value (AV) Theorem provide a major purpose of integrals. Be sure you understand the theorems and how to apply them.


By the end of this topic you should know and be prepared to be tested on:


Define: integrable, integrability, First Fundamental Theorem of Calculus (FTC1), Second Fundamental Theorem of Calculus (FTC2), Mean Value Theorem for Integrals, Average Value Theorem

Supplemental Resources (recommended)

Two applets for exploration: FTC 1 (theoretical part) and FTC 2 (practical part)

Supplemental Resources (optional)

Video: The Fundamental Theorem of Calculus, Selwyn Hollis's Video Calculus

Lesson: The Fundamental Theorem of Calculus, Dale Hoffman's Contemporary Calculus