   Chapter 13.2, Problem 29E ### 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

# Evaluate the definite integrals in Problems 1-32. 31.   ∫ 0 2 8 x 2 e − x 3   d x

To determine

To calculate: The value of the integral 028x2ex3dx.

Explanation

Given Information:

The provided integral is 028x2ex3dx.

Formula used:

To calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

For any variable u, the integral formula is

endu=en+C.

Derivative of xn with respect to x is, nxn1.

Calculation:

Consider the integral, 028x2ex3dx.

Recall that to calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

Thus, evaluate the integral.

Consider the expression, (x3).

Differentiate with respect to x.

d(x3)dx=3x2d(x3)=3x2dx

Thus, d(x3)=3x2dx.

Multiply and divide the integral by 3 and rewrite the integral as,

028ex3(3x23)dx

Now simplify further using, endu=en+C

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