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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. Evaluate the integral if it converges. See Examples 1, 2, and 3.

1 e x x d x

To determine

Whether the improper integral 1exxdx diverges or converges and evaluate if it converges.

Explanation

Given Information:

The provided expression is, 1exxdx

From definition of improper integral.

af(x)dx=limbabf(x)dx

Also, the expression for the integration of an exponential is as follows:

eaxdx=eaxa+C; where a0.

The improper integral converges if the limit exists otherwise the improper integral diverges.

Consider the provided expression:

1exxdx

Use the property of improper integral and simplify as:

1exxdx=limb1exxdx

Integrate the integrand by substation method as:

Assume ex=u

Differentiate as:

ex2xdx=du

Now, substitute the values and integrate as:

exxdx=2du=2u+C

Again, substitute the value of u

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