# To express the value of the integral. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 5.2, Problem 52E
To determine

## To express the value of the integral.

Expert Solution

The value of the integral is 250211+x2dx2 .

### Explanation of Solution

Given information:

The given equation is

0211+x2dx

Formula used:

Used the comparison property

if mf(x)M for axb,thenm(ba)abf(x)dxM(ba)

The value of the integral can be express as

Find a values of m and M

The values of a=0, b=2 and f(x)=11+x2

ba=20=2

Put the value of x=0 and x=2 in f(x)=11+x2

f(0)=11+02         =11         =1andf(2)=11+22         =11+4         =15

We have restricted function fand obtained value for

m=15 and M=1

Therefore,

According to comparison properties of integrals, we have

15(20)0211+x2dx1(20)=15(2)0211+x2dx1(2)=250211+x2dx2

Hence,

The value of the integral is 250211+x2dx2 .

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