   Chapter 5.3, Problem 80E ### 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

# (a) Show that cos(x2) ≥ cos x for 0 ≤ x ≤ 1.(b) Deduce that ∫ 0 π / 6 cos ( x 2 )   d x ≥ 1 2 .

(a)

To determine

To show: the expression cos(x2)cosxfor0x1.

Explanation

Given information:

Consider the following expression for the interval 0x1.

x2x

Consider the function f(x)=cosx is a decreasing function on interval [0,1].

f(x)2f

(b)

To determine

To deduce: the integral function 0π/6cos(x2)dx12.

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