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Luigi0210

  • 9 months ago

Integration:

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  1. Luigi0210
    • 9 months ago
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    \[\LARGE \int_{-1}^{0}~\frac{e^{1/x}}{x^3}~dx\]

  2. ganeshie8
    • 9 months ago
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    sub u = 1/x

  3. myininaya
    • 9 months ago
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    try letting u=1/x so x=1/u

  4. dan815
    • 9 months ago
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    then do parts

  5. Joshyboi25tolyfe
    • 9 months ago
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    Guys guys... In the eyes of god, mathematics doesn't exist! Now, let's all hold hands and pray.

  6. ganeshie8
    • 9 months ago
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    yeah u can't avoid parts i think

  7. dan815
    • 9 months ago
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    mathematics is a language and God gave us languages

  8. dan815
    • 9 months ago
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    so shut your 3.14 hole

  9. Joshyboi25tolyfe
    • 9 months ago
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    LOLOL ^

  10. dan815
    • 9 months ago
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    :)

  11. Luigi0210
    • 9 months ago
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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?

  12. Luigi0210
    • 9 months ago
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    *\[\LARGE -\int_{-1}^{0}~ue^udu\]

  13. myininaya
    • 9 months ago
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    you should have an improper integral

  14. Luigi0210
    • 9 months ago
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    \[\LARGE \LARGE \lim_{t \rightarrow 0} \int_{-1}^{t}~ue^udu~\]?

  15. myininaya
    • 9 months ago
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    of x is between -1 and 0 and u=1/x |dw:1402252341171:dw|

  16. myininaya
    • 9 months ago
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    as we approach 0 from the left what is u getting approaching?

  17. myininaya
    • 9 months ago
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    |dw:1402252495152:dw|

  18. myininaya
    • 9 months ago
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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

  19. myininaya
    • 9 months ago
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    i'm asking him to evaluate the following: \[\lim_{x \rightarrow 0^-}\frac{1}{x}\]

  20. myininaya
    • 9 months ago
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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?

  21. Luigi0210
    • 9 months ago
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    \(\Large -\infty\)?

  22. myininaya
    • 9 months ago
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    right so i'm going to change one thing in your lim from earlier \[\LARGE \LARGE \lim_{t \rightarrow - \infty} \int\limits_{-1}^{t}~ue^udu~ \]

  23. myininaya
    • 9 months ago
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    i think there should be a negative in front of that

  24. myininaya
    • 9 months ago
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    \[- \LARGE \LARGE \lim_{t \rightarrow - \infty} \int\limits\limits_{-1}^{t}~ue^udu~\]

  25. myininaya
    • 9 months ago
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    you know from the du=-1/x^2 dx thing

  26. myininaya
    • 9 months ago
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    now use integration by parts then evaluate the limit

  27. Luigi0210
    • 9 months ago
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    Alright, I see it now, it was the limits that was throwing me off >_< Thank you myininaya :)

  28. ganeshie8
    • 9 months ago
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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

  29. myininaya
    • 9 months ago
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    @Luigi0210 did you get it?

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