   Chapter 6, Problem 54RE ### 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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# Evaluating an Improper Integral In Exercises 51–56, determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∫ 0 ∞ e − 2 x   d x

To determine

To calculate: The value of the improper integral 0e2xdx if it converges.

Explanation

Given Information:

The provided expression is

0e2xdx

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:

eaxdx=eaxa+C

Here, a0

Calculation:

Consider the provided expression:

0e2xdx

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

And simplify as

"

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