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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Calculus I
Topic: Antiderivatives
Subtopic: Integration by Substitution & Definite Integrals

Overview

Integration by substitution is a method that allows us to “undo” the chain rule. The process involves making a u-substitution that enables a somewhat complicated integral to be rewritten as one that is simpler and can be easily integrated. The key lies in making the correct substitution!

We have used u-substitution method to evaluate indefinite integrals, but here we use it to evaluate definite integrals. Note that with indefinite integrals at the end of the process we convert back to in terms of x, but with definite integrals we convert everything to in terms of u, including the limits of integration, and never return to x.

Objectives

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

Terminology

Define: convert limits of integration to "in terms of u"

Supplemental Resources (optional)

Video: Change of Variables (Substitution), Selwyn Hollis's Video Calculus

Lesson: First Applications of Definite Integrals, Dale Hoffman's Contemporary Calculus includes a variety of applications for motivation for the transition from Calc I to Calc II.