   Chapter 13.6, Problem 28E ### 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 25-30, select the formula or method (I-IV) that should be used to evaluate each integral. Then evaluate the integral.I. Integration by partsII. ∫ e u d u III. ∫ d u u IV. ∫ u n d u ∫ 4 x 2 e x 3 d x

To determine

To calculate: The value of the integral 4x2ex3dx.

Explanation

Given Information:

The provided integral is 4x2ex3dx.

Formula used:

According to the exponential rule of integrals,

eudu=eu+C

Differential formula,

d(xn)dx=nxn1

Calculation:

Consider the provided integral:

4x2ex3dx

The integral is similar to the formula eudu.

Now to evaluate further,

Divide and multiply by 3 to rewrite the integral as

433x2ex3dx

Now, let x3=u, and differentiate by the use of differential formula d(xn)dx=nxn1,

3x2dx=du

Thus, the integral becomes,

433x

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