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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 7–20, determine whether the improper integral diverges or converges. See Example 1, 2, and 3.

0 7 x ( 3 x 2 + 5 ) 2 d x

To determine

To calculate: Whether the improper integral 07x(3x2+5)2dx diverges or converges and evaluate if it converges.

Explanation

Given Information:

The integral is provided as:

07x(3x2+5)2dx.

Formula used:

From definition of improper integral.

af(x)dx=limbabf(x)dx

Calculation:

Consider the provided integral:

07x(3x2+5)2dx

Use the property of improper integral af(x)dx=limbabf(x)dx and simplify as:

07x(3x2+5)2dx=limb0b7x(3x2+5)2dx

Integrate the integrand by substation method as:

Assume 3x2+5=u

Differentiate as:

6xdx=du

Now, substitute the values and integrate as:

7x(3x2+5)2dx=421u2du=423u3+C

Again, substitute the value of u

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