   Chapter 4.2, Problem 56E

Chapter
Section
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 011+x2dx011+xdx without evaluating the integrals

Solution:In the following we verify that

011+x2dx 011+x dx

Explanation

1) Concept:

Use thecomparison property (7) of the integral.

if fxg(x) for axb thenabfxdxabgxdx

2) Calculation:

Here,x2x    for x[0, 1]

So from theabove step

1+x21+x  for x[0,

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