Chapter 13, Problem 33RE

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the improper integrals in Problems 31-34. ∫ 0 ∞ 5 e − 3 x   d x

To determine

To calculate: The value of the improper integral 05e3xdx if it converges.

Explanation

Given Information:

The provided integral is,

05e3xdx

Formula used:

According to the exponential rule of integrals,

exdx=ex+C

If the limit defining the improper integral is a unique finite number, then integral converges else it diverges,

af(x)dx=limbabf(x)dx

Calculation:

Consider the provided integral,

05e3xdx

Now, use the formula,

af(x)dx=limbabf(x)dx

To rewrite the integral as,

05e3xdx=limb

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