   Chapter 6, Problem 12RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Evaluating a Definite Integral In Exercises 9-12, use integration by parts to evaluate the definite integral. ∫ − 1 1 x 2 e 3 x d x

To determine

To calculate: The value of the definite integral by integration by parts:

11x2e3xdx

Explanation

Given Information:

Consider the integral:

11x2e3xdx

Formula used:

The formula for the integration by parts is:

udv=uvvdu

The integral of an exponential is:

eaxdx=eaxa+C

Here, C is integration constant.

Calculation:

Consider the integral and solve as,

11x2e3xdx

Assume dv=e3x

Integrate,

dv=e3xdtv=e3x3

And assume u=x2.

Differentiate,

du=2xdx

Use integration by parts to integrate udv=uvvdu.

x2e3xdt=13x2e3x23[xe3xdx]

Again, assume dv=e3x

Integrate,

dv=e3xdtv=e3x3

And assume u=x

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