Improper Integral

Kcashew

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Mar 17, 2020
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Good morning everyone.

I hope I can get some help on this problem.

I believe I have taken the integral correctly, but I do not know how to implement infinity into it.

How should I go about solving this?
 

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pka

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What is the limit as \(b\to\infty~?\)
 

Kcashew

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Yes, that is correct
 

Kcashew

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What is the limit as \(b\to\infty~?\)
WAIT SORRY I misread that

What I meant to say was, I do not know how to compute that.
 

Jomo

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Please write down the limit you are having trouble with, so everyone is on the same page, state why you are having trouble and you will be expertly helped. Fair enough?
 

pka

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WAIT SORRY I misread that What I meant to say was, I do not know how to compute that.
\(\displaystyle\left. { - {e^{ - x}}(x + 1)} \right|_0^b = \left[ { - {e^{ - b}}(b + 1)} \right] - \left[ { - 1(1)} \right]\)
Now what is the limit as \(b\to\infty \)
 

Kcashew

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Please write down the limit you are having trouble with, so everyone is on the same page, state why you are having trouble and you will be expertly helped. Fair enough?
This was what I was having trouble with

\(\displaystyle\left. { - {e^{ - x}}(x + 1)} \right|_0^b = \left[ { - {e^{ - b}}(b + 1)} \right] - \left[ { - 1(1)} \right]\)
Now what is the limit as \(b\to\infty \)
 

Kcashew

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I believe that the limit would be 1, considering that E is raised to the power of negative infinity
 

pka

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