   Chapter 6.1, Problem 5CP ### 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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# Checkpoint 5Use the result of Example 4 to evaluate ∫ 0 1 x 2 e x d x .

To determine

To calculate: The value of definite integral 01x2exdx.

Explanation

Given Information:

The provided definite integral is 01x2exdx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

eaxdx=eaxa+C

Calculation:

Consider the definite integral 01x2exdx

Here,

dv=exdx and u=x2

First find v,

dv=exdxdv=exdx

On further solving,

v=ex …… (1)

Now find du,

u=x2

Differentiate both side with respect x,

dudx=d(x2)dxdudx=2x

And,

du=2xdx …… (2)

Apply integration by parts formula and substitute equation (1) and (2) in udv=uvvdu,

x2exdx=x2ex2xexdx

Use integration by parts on the second integral xexdx

Here,

dv=exdx and u=x

First find v,

dv=exdxdv=exdx</

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