   Chapter 13.5, Problem 20E ### 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 1-32. Identify the formula used. ∫ x   e x 2 d x

To determine

To calculate: The value of integral xex2dx.

Explanation

Given Information:

The provided integral is xex2dx.

Formula used:

For any variable u, the integral formula is,

eudu=eu+C

Differentiation of un with respect to u is nun1.

Where n is any real number

Calculation:

Consider the provided integral:

xex2dx

Multiply and divide the integral by 2.

12ex2(2xdx)

Let x2=t

Differentiate both the sides,

2xdx=dt

Now, the integral becomes,

12etdt

The integral is similar to the integral formula,

eudu

Therefore, the formula used is eudu=eu+C

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