   Chapter 6, Problem 60RE ### 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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# Area of a Region In Exercises 57–60, find the area of the unbounded shaded region. y = 4 x e − 2 x 2 To determine

To calculate: The area under the shaded region by the graph of the equation y=4xe2x2 Explanation

Given Information:

The equation of the graph that provides shaded region is y=4xe2x2 and the graph is,

Formula used:

From definition of improper integral.

If on the interval [a,), the function is continuous, then

af(x)dx=limbabf(x)dx

The integral formula:

eax=eaxa+C

Calculation:

Consider the provided equation:

04xe2x2dx

And the graph is,

Use the definition of improper integral af(x)dx=limbabf(x)dx

And simplify as

04xe2x2dx=limb0b4xe2x2dx

In the provided integral,

Assume 2x2=u

Now, differentiate

4xdx=du

Now, substitute the

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