   Chapter 5, Problem 63RE ### 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

# If f is continuous and ∫ 0 2 f ( x )   d x = 6 , evaluate ∫ 0 π / 2 f ( 2 sin θ ) cos θ   d θ .

To determine

To calculate: The value of the integral function 0π/2f(2sinθ)cosθdθ.

Explanation

Given information:

The integral function is 0π/2f(2sinθ)cosθdθ (1)

The value of the integral function 02f(x)dx is 6.

Consider x=2sinθ (2)

Differentiate both sides of the Equation (2).

dxdθ=ddθ(2sinθ)=2cosθ

Calculate the lower limit value of x using Equation (2).

Substitute 0 for θ in Equation (2).

x=2sin0=0

Calculate the upper limit value of u using Equation (2).

Substitute π2 for θ in Equation (2)

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