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Luigi0210
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\[\LARGE \int_{-1}^{0}~\frac{e^{1/x}}{x^3}~dx\]
ganeshie8
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sub u = 1/x
myininaya
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try letting u=1/x
so x=1/u
dan815
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then do parts
Joshyboi25tolyfe
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Guys guys... In the eyes of god, mathematics doesn't exist! Now, let's all hold hands and pray.
ganeshie8
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yeah u can't avoid parts i think
dan815
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mathematics is a language and God gave us languages
dan815
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so shut your 3.14 hole
Joshyboi25tolyfe
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LOLOL ^
dan815
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:)
Luigi0210
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\[\LARGE \int_{-1}^{0}~\frac{e^{1/x}}{x^3}~dx\]
\[\LARGE =\int_{-1}^{0}~\frac{1}{x}~e^{1/x}~\frac{1}{x^2}~dx\]
\(\Large u=1/x\) and \(\Large du=-\frac{1}{x^2}dx\)
\[\LARGE \int_{-1}^{0}~ue^udu\]
And then use parts like dan said?
Luigi0210
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*\[\LARGE -\int_{-1}^{0}~ue^udu\]
myininaya
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you should have an improper integral
Luigi0210
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\[\LARGE \LARGE \lim_{t \rightarrow 0} \int_{-1}^{t}~ue^udu~\]?
myininaya
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of x is between -1 and 0
and u=1/x
|dw:1402252341171:dw|
myininaya
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as we approach 0 from the left what is u getting approaching?
myininaya
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|dw:1402252495152:dw|
myininaya
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we are looking to the left of 0 because our interval is -1 to 0
none of our values occur to the right of 0 so we won't bother to look there
myininaya
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i'm asking him to evaluate the following:
\[\lim_{x \rightarrow 0^-}\frac{1}{x}\]
myininaya
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lugi0210 just read the graph above
as our x values get near the 0 number (from the left)
what do your u values (or if you want call them y values) do?
Luigi0210
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\(\Large -\infty\)?
myininaya
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right
so i'm going to change one thing in your lim from earlier
\[\LARGE \LARGE \lim_{t \rightarrow - \infty} \int\limits_{-1}^{t}~ue^udu~ \]
myininaya
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i think there should be a negative in front of that
myininaya
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\[- \LARGE \LARGE \lim_{t \rightarrow - \infty} \int\limits\limits_{-1}^{t}~ue^udu~\]
myininaya
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you know from the du=-1/x^2 dx thing
myininaya
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now use integration by parts
then evaluate the limit
Luigi0210
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Alright, I see it now, it was the limits that was throwing me off >_<
Thank you myininaya :)
ganeshie8
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if u feel lazy about changing the bounds, you may try below :
1) Find the indefinite integral first
2) plugin the bounds
myininaya
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@Luigi0210 did you get it?