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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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

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

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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 ∫0∞ce0.5tdt=1.

Explanation

Given Information:

The provided integral is,

∫0∞ce0.5tdt

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,

∫a∞f(x)dx=limb→∞∫abf(x)dx

Calculation:

Consider the provided integral,

∫0∞ce0.5tdt

Now, use the formula,

∫a∞f(x)dx=limb→∞∫abf(x)dx

To rewrite the integral as,

∫0∞ce0.5tdt=limb→∞∫0bce0.5tdt

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

limb→∞∫0bce0.5tdt=limb→∞∫0bce−0

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Chapter 13.7,
Problem 20E
Chapter 13.7,
Problem 22E
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