   Chapter 13.7, Problem 2CP ### 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 following (if they exist).(a) ∫ 1 ∞ 1 x 4 / 3 d x = lim b → ∞ ∫ 1 b x − 4 / 3 d x (b) ∫ 0 ∞ d x x + 1

(a)

To determine

To calculate: The value of the improper integral 1dxx4/3 if it converges.

Explanation

Given Information:

The provided integral is,

1dxx4/3

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,

1dxx4/3

Now, use the formula,

af(x)dx=limbabf(x)dx

To rewrite the integral as,

1dxx4/3=limb1bx4/3dx

Now, use the power rule of integrals to obtain this integral as,

1dx

(b)

To determine

To calculate: The value of the improper integral 01x+1dx if it converges.

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