   Chapter 13.7, Problem 21E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# For what value of c does ∫ 0 ∞ c e 0.5 t d t = 1 ?

To determine

To calculate: The value of c for which 0ce0.5tdt=1.

Explanation

Given Information:

The provided integral is,

0ce0.5tdt

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,

0ce0.5tdt

Now, use the formula,

af(x)dx=limbabf(x)dx

To rewrite the integral as,

0ce0.5tdt=limb0bce0.5tdt

Now, use the exponential rule of integrals to obtain the value of c as,

limb0bce0.5tdt=limb0bce0

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