Integration by Substitution

Integration by Substitution Integration by Substitution - Start

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Integration by Substitution - Description

Section 6.2a. A change of variables can often turn an. unfamiliar integral into one that we can. evaluate…. This method is called the. substitution method of integration.. The New Method. The New Method. ID: 585331 Download Presentation

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Integration by Substitution




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Presentations text content in Integration by Substitution

Slide1

Integration by Substitution

Section 6.2a

Slide2

A change of variables can often turn anunfamiliar integral into one that we canevaluate…

This method is called thesubstitution method of integration.

The New Method

Slide3

The New Method

Generally, this method is used when integrating a compositefunction, and the derivative of the inside function is alsopresent in the integrand:

1. Substitute

u

= g(x), du = g (x)dx

2. Evaluate by finding an

antiderivative

F (u) of f (u)

3. Replace

u

by

g

(

x

)

Slide4

Initial Practice Problems

Evaluate

Let

Then

Substitute:

(Substitute)

Slide5

Initial Practice Problems

Evaluate

Let

Then

Substitute:

Slide6

Initial Practice Problems

Evaluate

Let

Then

Substitute:

Slide7

Initial Practice Problems

Evaluate

Let

Then

Substitute:

Slide8

Substitution in Definite Integrals

Instead of the last step we’ve been using (re-substitution???):

Substitute , and integrate with

respect to

u

from to .

Slide9

Evaluating Definite Integrals

Evaluate

Let

Then

Also, notice:

Substitute:

Slide10

Two Possible Methods?

Evaluate

Let

Then

Also, notice:

Method 1

Substitute:

Slide11

Two Possible Methods?

Evaluate

Let

Then

Substitute:

Method

2

Slide12

Guided Practice

Evaluate the given integral.

Slide13

Guided Practice

Evaluate the given integral.

Slide14

Guided Practice

Evaluate the given integral.

Slide15

Guided Practice

Evaluate the given integral.

Slide16

Guided Practice

Evaluate the given integral.


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