8.1: Integration by Substitution
This activity is intended to supplement Calculus, Chapter 7, Lesson 1.
In this activity, you will explore:
 Integration of standard forms
 Substitution methods of integration
Use this document to record your answers. Check your answers with the Integrate command.
Problem 1 – Introduction
1. Consider the integral
Use the table below to guide you.












2. Try using substitution to integrate
3. Now integrate the same integral, but let
4.
What is the result when you integrate
Problem 2 – Common Feature
Find the result of the following integrals using substitution.
5.
6.
7.
8. What do these integrals have in common that makes them suitable for the substitution method?
Extension
Use trigonometric identities to rearrange the following integrals and then use the substitution method to integrate.
9.
10.
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