Chapter 9.2, Problem 7SWU

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

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# In Exercises 5-7, evaluate the definite or improper integral. ∫ 0 ∞ 3 e − 3 t d t

To determine

To calculate: The solution of the improper integral 03e3tdt

Explanation

Given Information:

The provided improper integral is 03e3tdt.

Formula used:

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

af(x)dx=limbabf(x)dx

According to the exponential rule of integrals,

exdx=ex+C

Calculation:

Consider the given equation,

I=03e3t

Now, use the formula, af(x)dx=limbabf(x)dx to rewrite the integral as,

I=03e3t=limb0b3e3tdx

Now, integrate,

I=limb0b3eȡ

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