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Richa Nandra, Lovely Professional University Unit 5: Definite Integrals by Substitution

Unit 5: Definite Integrals by Substitution Notes

CONTENTS
Objectives
Introduction

5.1 Substitution Rule for Definite Integrals
5.2 Use Substitution to Find Definite Integrals
5.3 Summary

5.4 Keyword
5.5 Review Questions
5.6 Further Readings

Objectives

After studying this unit, you will be able to:

 Understand the Substitution rule for definite integrals
 Discuss the concept of definite integrals by substitution

Introduction

As we know, the first step in performing a definite integral is to calculate the indefinite integral
and that hasn’t tainted. We will still calculate the indefinite integral initially. This signifies that
we by now know how to perform these. Now, in this unit, we make use of the substitution rule
to locate the indefinite integral and then perform the evaluation.
5.1 Substitution Rule for Definite Integrals

There are though, two methods to treat with the assessment step.
The steps for performing integration by substitution for definite integrals are the similar as the
steps for integration by substitution for indefinite integrals apart from we must alter the bounds
of integration and we do not require subbing back in for u.
1. Let u = g (x).

2. Find du/dx = g’ (x)
3. Let du = g’ (x) dx. Now, confirm that this is included in the unique integral. If not, then you
cannot utilize this method.

4. Substitute u in for g (x) and du in for g’ (x) dx.
5. Locate the new bounds of integration by plugging in the lower bound into u. That
consequence will be the new lower bound. Then plug in the upper bound into u. This will
be the new upper bound.
6. Integrate the new integral.
7. Plug in the new bounds and calculate.

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