   Chapter 4.2, Problem 68E

Chapter
Section
Textbook Problem

# Which one of the integrals ∫ 0 0.5 cos ( x 2 ) d x ,   ∫ 0 0.5 cos x   d x is larger?

To determine

The larger integral from 00.5cosx2dx  and  00.5cosx dx

Explanation

1) Concept:

Comparison Property of integral:

If fxgx for axb, then abfxdx abgxdx

2) Calculation:

For 0<x0.5,      x2<x

Cosine function is decreasing on 0 ,π21.57

So, it is decreasing on 0, 0.5

Thus we have

cos(x2) >cos(x )

Now use the comparison property oftheintegral

00

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Change 3 lb to ounces.

Elementary Technical Mathematics

#### Evaluate the integral. 26. 12w2lnwdw

Single Variable Calculus: Early Transcendentals

#### The polar form for the graph at the right is:

Study Guide for Stewart's Multivariable Calculus, 8th 