   Chapter 5, Problem 2RQ ### 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 and g are continuous on [a, b], then ∫ a b [ f ( x ) + g ( x ) ]   d x = ( ∫ a b f ( x )   d x ) ( ∫ a b g ( x )   d x )

To determine

Whether the statement ab[f(x)g(x)]dx=(abf(x)dx)+(abg(x)dx) is true or false.

Explanation

Given information:

The function is ab[f(x)g(x)]dx=(abf(x)dx)+(abg(x)dx) (1)

Calculation:

Check the statement is true or false using an example as shown below:

Let assume a=0,b=2,andf(x)=g(x)=1.

Find the integral value of left hand side part in Equation (1).

Substitute 0 for a, 2 for b, 1 for f(x), and 1 for g(x) in Equation (1).

ab[f(x)g(x)]dx=02dx=[x]02=20=2 (2)

Find the integral value of right hand side part in Equation (1).

Substitute 0 for a, 2 for b, 1 for f(x), and 1 for g(x) in Equation (1)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### True or False: If f(x) 0 for all x in an interval I then f is increasing on I.

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

#### True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

#### Solve each equation. x4+36=13x2

College Algebra (MindTap Course List) 