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Math Help - Double Integral Problem

  1. #1
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    Double Integral Problem

    Hello, I am having difficulty setting up this double integral.

    f(s,t)=e^slnt over the region in the first quadrant of the st plane that lies above the curve s=lnt from t=1 to t=2

    so far I have converted the s=lnt into the format: t=e^s Then I graphed it, and for my bound on my integral, I got: \int_1^2\int_o^{e^s}{e^slnt} dtds

    Nevermind....after trying numerous different things, I think I have finally found the right answer. The x bounds were really getting me. I knew the y bounds had to be 1 and 2, since that was given, but for some reason, the x bounds were giving me trouble.

    \int_1^2\int_o^{lny}{e^slnt} dtds
    Last edited by BCHurricane89; November 29th 2009 at 05:08 PM.
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  2. #2
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    Quote Originally Posted by BCHurricane89 View Post
    \int_1^2\int_o^{e^s}{e^slnt} dtds

    It is wrong ( just my view )

    I think the correct boundary is

     1 \leq t \leq 2   ,  0 \leq s \leq <br />
ln(t)


    so what we have to calculate is

     \int_1^2\int_0^{\ln(t)} e^s \ln(t)~dsdt

    integrate w.r.t. s first .


     = \int_1^2 \ln(t) [ e^s ]_0^{\ln(t)} ~dt

     = \int_1^2 (t-1)\ln(t)~dt = [(t-1)^2\ln(t)/2 - t^2/4 + t - \ln(t)/2 ]_1^2

     = 2  - 1 + 1/4 -1  = 1/4
    Last edited by simplependulum; November 30th 2009 at 02:17 AM.
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  3. #3
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    - Wolfram|Alpha


    It tells us the answer but no steps are shown ( pity ) .

    I think it is easy to input ... so why not you check your exercises online
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