# 8.1: Integration by Substitution

Difficulty Level: At Grade Created by: CK-12

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

## Problem 1 – Introduction

1. Consider the integral . Let . Evaluate the integral using substitution.

Use the table below to guide you.

2. Try using substitution to integrate . Let .

3. Now integrate the same integral, but let . How does the result compare to the one above?

4. can be rewritten as using the Double Angle formula.

What is the result when you integrate using substitution?

## 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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