   Chapter 5, Problem 15P ### 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

# Prove that if f is continuous, then ∫ 0 x f ( u ) ( x − u )   d u = ∫ 0 x ( ∫ 0 u f ( t )   d t )   d u .

To determine

To prove: The value of the integral function 0xf(u)(xu)du=0x(0uf(t)dt)du.

Explanation

Given information:

The integral function is 0xf(u)(xu)du.

Calculation:

Consider the integral function as follows:

0xf(u)(xu)du (1)

Apply the Fundamental Theorem of calculus 1 as shown below.

ddx(0x[0uf(t)dt]du)=0xf(t)dt

Apply the fundamental Theorem of Calculus 1 in Equation (1).

ddx(0xf(u)(xu)du)=dds[x0xf(u)du]dds[0xf(u

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