   Chapter 13.7, Problem 10E ### 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

# In Problems 1-20, evaluate the improper integrals that converge. 10.   ∫ 1 ∞ x e x 2   d x

To determine

To calculate: The value of the improper integral 1xex2dx.

Explanation

Given Information:

The provided integral is,

1xex2dx

Formula used:

According to the exponential rule of integrals,

exdx=ex+C

If the limit defining the improper integral is a unique finite number, then integral converges else it diverges,

af(x)dx=limbabf(x)dx

Calculation:

Consider the provided integral,

1xex2dx

Now, use the formula,

af(x)dx=limbabf(x)dx

Multiply and divide by 2 and write the integral as,

1xex2dx=12limb1b2xex2dx

Now, let x2=t, and then differentiate both the sides,

2xdx=dt

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