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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Evaluating an Improper Integral In Exercises 51–56, determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

1 1 x 4 d x

To determine

To calculate: The value of integral 11x4dx if it converges.

Explanation

Given Information:

The provided expression is,

11x4dx

Formula used:

From definition of improper integral.

If on the interval [a,), the function is continuous, then

af(x)dx=limbabf(x)dx

Here, the improper integral converges if the limit exists and otherwise it diverges.

The integral formula:

xndx=xn+1n+1+C

Calculation:

Consider the provided expression,

11x4dx

Use the definition of improper integral af(x)dx=limbabf(x)dx

And simplify as

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