   Chapter 5, Problem 69RE ### 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 on [a, b] show that 2 ∫ a b f ( x ) f ′ ( x ) d x = [ f ( b ) ] 2 − [ f ( a ) ] 2

To determine

To evaluate: The integral function 2abf(x)f(x)dx.

Explanation

Given information:

The integral function is 2abf(x)f(x)dx (1)

Consider u=f(x) (2)

Differentiate both sides of the Equation (2).

du=f(x)dx

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

Substitute a for x in Equation (2).

u=f(a)

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

Substitute b for x in Equation (2).

u=f(b)

Substitute u for f(x) and du for f(x) in Equation (1) as shown below

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 