Chapter 13.7, Problem 1E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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. 1.   ∫ 1 ∞ d x x 6

To determine

To calculate: The value of the improper integral 1dxx6 if it converges.

Explanation

Given Information:

The provided integral is,

1dxx6

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,

1dxx6

Now, use the formula,

af(x)dx=limbabf(x)dx

To rewrite the integral as,

1dxx6=limb1b

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