   Chapter 5, Problem 55RE ### 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. ∫ 0 1 e x cos x   d x ≤ e − 1

To determine

To verify: The inequality of the integral function using the properties of integrals.

Explanation

Given information:

The integral function is 01excosxdx.

The region lies between x=0 and x=1.

Calculation:

Consider the function f(x)=excosx (1)

Apply Property 8 of integrals as follows:

If mf(x)M for axb, then m(ba)abf(x)dxM(ba).

Find the absolute maximum value M as shown below:

Substitute 0 for x in Equation (1).

M=f(0)=e0cos(0)=1

Find the absolute minimum value m as shown below:

Substitute 1 for x in Equation (1).

m=f(1)=e1cos(1)=0

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