   Chapter 5.5, Problem 87E ### 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 4 f ( x )   d x = 10 , find ∫ 0 2 f ( 2 x )   d x .

To determine

To find: The integral value.

Explanation

Given:

If f is continuous and 04f(x)dx=10.

The integral function is 02f(2x)dx.

The region lies between x=0 and x=2.

Calculation:

Take the consideration as follows:

u=2x (1)

Differentiate both sides of the Equation (1).

du=2dxdx=12du

Calculate the lower limit value of u using Equation (1).

Substitute 0 for x in Equation (1).

u=2(0)=0

Calculate the upper limit value of u using Equation (1).

Substitute 2 for x in Equation (1).

u=2(2)=4

The integral function is,

02f(2x)dx (2)

Apply lower and upper limits for u in Equation (2)

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