   Chapter 7.1, Problem 31E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 1 5 M e M d M

To determine

To evaluate: The given integral using the technique of integration by parts.

Explanation

The technique of integration by parts comes in handy when the integrand involves product of two functions. It can be thought of as a rule corresponding to the product rule in differentiation.

Formula used:

The formula for integration by parts for definite integral is given by

abf(x)g(x)dx=f(x)g(x)]ababg(x)f(x)dx

Given:

The integral, 15MeMdM.

Calculation:

Make the choice for u and dv such that the resulting integration from the formula above is easier to integrate. Let

u=M      dv=1eMdM

Then, the differentiation of u and antiderivative of dv will be

du=dM     v=eM

Usingthe formula above, the given integration will become

15MeMdM=M(eM)]1515(eM)dM=M(eM

### 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 