   Chapter 5.2, Problem 56E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Use the properties of integrals to verify the inequality without evaluating the integrals. ∫ 0 1 1 + x 2 d x ≤ ∫ 0 1 1 + x ​ ​ ​   d x

To determine

To verify: The inequality of the integral function 011+x2dx011+xdx using the properties of integrals.

Explanation

Given information:

The integral function is 011+x2dx011+xdx.

Consider the function f(x)=1+x2 and g(x)=1+x with limits [a,b] as [0,1].

Apply Property 7 of integrals:

If f(x)g(x) for axb, then abf(x)dxabg(x)dx.

Calculation:

Check the condition to apply property 7.

f(x)g(x) (1)

Substitute 0 for x in Equation (1).

f(0)g(0)1+01+011

Substitute 1 for x in Equation (1)

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