   Chapter 12.2, Problem 22E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the integrals in Problems 7-36. Check your results by differentiation. ∫ 3 x 5 − x 2 d x

To determine

To calculate: The value of the integral 3x5x2dx and also check the solution by differentiation.

Explanation

Given Information:

The provided integral is 3x5x2dx.

Formula used:

According to the power formula of integrals, if u=u(x), then,

undu=un+1n+1+C

According to the power rule of derivative,

ddx(xn)=nxn1

Calculation:

Consider the provided integral,

3x5x2dx

Rewrite the integral by multiplying and dividing by 2 as,

32(2x)5x2dx

Consider the power rule of integrals,

undu=un+1n+1+C

Now, to use the power rule, the integrand should have the function u(x) and its derivative u(x) and n1.

Let, u=5x2 and n=12

Differentiate u=5x2 with respect to x and get,

du=2xdx

Now, all required parts are present, so the integral is of the form,

32(2x)5x2dx=32

### 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

#### Find more solutions based on key concepts 