   Chapter 5, Problem 4RQ ### 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

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is continuous on [a, b], then ∫ a b x f ( x )   d x = x ∫ a b f ( x )   d x

To determine

whether the given statement is true or false.

Explanation

Given information:

Show the given function as follows:

abxf(x)dx=xabf(x)dx (1)

Equation (1) is valid, if f is continuous on [a,b].

Explanation for justification of statement:

Calculation:

Consider f(x)=1 on [0,1].

Consider upper limit b as 1 and lower limit a as 0.

Substitute 1 for f(x), 0 for a, and 1 for b in Equation (1).

01x(1)dx=x01(1)dx (2)

Evaluate the part of the integral 01x(1)dx from Equation (2).

01x(1)dx=01xdx=(x22)01=12 (3)

Evaluate the part of the integral x01(1)dx from Equation (2)

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