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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Evaluating a Definite Integral In Exercises 39-46, use integration by parts to evaluate the definite integral. See Example 5.

0 4 x e x / 2 d x

To determine

To calculate: The value of definite integral 04xex2dx.

Explanation

Given Information:

The provided definite integral is 04xex2dx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

eaxdx=1aeax+C

Calculation:

Consider the definite integral 04xex2dx

The above definite integral can be written as,

04xex2dx=04xex2dx

Here,

dv=ex2dx and u=x

First find v,

dv=ex2dxdv=ex2dx

On further solving,

v=2ex2 …...…... (1)

Find du:

u=x

Differentiate both side with respect x;

dudx=d(x)dxdudx=1

And,

du=1dx …...…..

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