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Math Help - Line integral troubles

  1. #1
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    Line integral troubles

    Evaluate the line integral, where C is the given curve.

    C xe^y dx, C is the arc of the curve x = e^y from (1, 0) to (e^4, 4)

    Here is my work, which results in some absurdly large number (comparable to the number of atoms in the visible universe) that I know cannot possibly be the answer.

    I'm fairly certain I don't have to parametrize (I don't see why I should), but I did anyways. I'd get the same answer regardless. The integration was done in WolframAlpha to ensure at least that part is correct, though I obviously have an incorrect integrand.



    I was going to integrate with respect to y, but I saw that "dx" in the original integral and integrated with respect to x. I tried y anyways, and still came up with a wrong answer.

    Any help would be amazing.

    Thanks.
    Last edited by tangibleLime; April 27th 2011 at 02:15 PM.
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  2. #2
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    Why would you parameterize in terms of 't' and then fail to use 't' in your limits of integration?

    It seems to me that your off-handed discarding of the parameterization ("not even needed") and your casual use of 'x' for limits may be misguided.

    Try t in [0,4] You may notice that this is [ln(e^0),ln(e^4)]. If you examine the relationship between x and t, this should be the relationship.
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  3. #3
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    Hm... I was following an example of the book, where they simply left x in terms of y and used y=y instead of y=t, but I may be mistaken about it's significance.

    Regardless, I still don't think I fully understand what I'm doing here, mainly in terms of the integration limits (which I am sure is what is giving me the wrong answer).. here's my latest attempt that once again revealed an incorrect answer.





    EDIT:

    Okay, I got it.

    Last edited by tangibleLime; April 27th 2011 at 04:27 PM.
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