   Chapter 15, Problem 5RQ

Chapter
Section
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 [0, 1], then ∫ 0 1   ∫ 0 1 f ( x )   f ( y )     d y   d x   =   [ ∫ 0 1 f ( x ) ​   d x ] 2

To determine

Whether the statement, “ 0101f(x)f(y)dydx=[01f(x)dx]2 ” is true or false.

Explanation

Formula used:

If g(x) is the function of x and h(y) is the function of y then,

abcdg(x)h(y)dydx=abg(x)dxcdh(y)dy (1)

Change of variables doesn’t affect the value of the integral, that is abf(x)dx=abf(y)dy

Reason:

By the equation (1), separate the given integrals

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

Draw, in standard position, the angle whose measure is given. 17. 315

Single Variable Calculus: Early Transcendentals, Volume I

Solve the equations in Exercises 126. x+4x+1+x+43x=0

Finite Mathematics and Applied Calculus (MindTap Course List)

In problems 31-36, simplify each expression. 33.

Mathematical Applications for the Management, Life, and Social Sciences

Find the limit. limx(x2+4x+1x)

Single Variable Calculus: Early Transcendentals 