BuyFind

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter 5.2, Problem 51E
To determine

To verify the equation.

Expert Solution

Explanation of Solution

Given information:

The given equation is

  2111+x2dx22

Formula used:

Used the comparison property

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

Proof:

The equation can be verified as

For (1x1) , we can say

  0x2111+x22              [add 1 all side]11+x22     [take square root]

According to comparison properties of integrals, we have

  1(1(1))111+x2dx2(1(1))1(1+1)111+x2dx2(1+1)1(2)111+x2dx2(2)2111+x2dx22

Hence,

The equation is verify.

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