   Chapter 6, Problem 14TYS ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# In Exercises 14–17, determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∫ 0 ∞ e − 3 x d x

To determine

Whether the improper integral 0e3xdx diverges or converges and evaluate if it converges.

Explanation

Consider the provided integral:

0e3xdx

From definition of improper integral.

af(x)dx=limbabf(x)dx

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

eaxdx=eaxa+C

Here, a0.

Use the property of improper integral and simplify as:

0e3dx=limb0be3dx

Use the formula for polynomial to integrate the above integral

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