   Chapter 13.7, Problem 4E ### 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 1-20, evaluate the improper integrals that converge. 4.   ∫ 5 ∞ d x ( x − 1 ) 3   d x

To determine

To calculate: The value of the improper integral 5dx(x1)3 if it converges.

Explanation

Given Information:

The provided integral is,

5dx(x1)3

Formula used:

According to the power rule of integrals,

xndx=xn+1n+1+C

If the limit defining the improper integral is a unique finite number, then integral converges else it diverges,

af(x)dx=limbabf(x)dx

Calculation:

Consider the provided integral,

5dx(x1)3

Now, use the formula,

af(x)dx=limbabf(x)dx

To rewrite the integral as,

5dx(x1)3=limb5b(x1)3dx

Now, use the power rule of integrals to evaluate the integral,

5dx

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