   Chapter 8, Problem 69RE

Chapter
Section
Textbook Problem

Evaluating a Definite Integral In Exercises 69-74, evaluate the definite integral using any method. Use a graphing utility to verify your result. ∫ 2 5 x ( x 2 − 4 ) 3 / 2 d x

To determine

To calculate: The value and verify the result using a graphing utility of definite integral 25x(x24)3/2dx.

Explanation

Given: We are given with the Definite Integral 25x(x24)3/2dx.

Formula used:

Substitution method.

Calculation:

Let I=25x(x24)3/2dx

Put x2=t

On Differentiating both sides, we get that:

2xdx=dt

x2,t4andx5,t5

On substituting, we get that:

I=1245(t4)3/2dt=12(25(t4)5/2)45=15((1)5/20)=0

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