   Chapter 8, Problem 86RE

Chapter
Section
Textbook Problem

Evaluating an Improper Integral In Exercises 79-86, determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∫ 0 ∞ 2 x ( x + 4 )   d x

To determine

To calculate: whether the integral 02x(x+4)dx converges or diverges. Evaluate if it is converges.

Explanation

Given: We are given with the expression 02x(x+4)dx.

Formula used:

abf(x)dx=acf(x)dx+cbf(x)dx

Calculation:

Since f(x)=02x(x+4)dx is continuous in (0,)

Therefore,

02x(x+4)dx=012x(x+4)dx+12x(x+4)dx

For I=02x(x+4)dx

Put

x=tx=t2

On Differentiating both sides, we get that:

dx=2tdt

Therefore,

I=22tdtt(

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