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Math Help - Integration (3)

  1. #1
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    Integration (3)

    A curve is defined by the following pair of parametric equations:

    x = t(e^t) and y = t sin t , t>0. Find the area of the region enclosed by the curve, the x-axis and the line x = e.

    Thank you!
    Last edited by Tangera; August 17th 2008 at 02:37 AM.
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  2. #2
    Super Member wingless's Avatar
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    First plot to curve to make sure we set the integral correctly.



    Now we can set the integral.

    \int_0^e y~dx

    \int_0^e t \sin t~d(t e^t)

    \int_0^1 t \sin t (e^t + t e^t)~dt (the bounds of integration changes because of the differential dx -> dt)

    I guess you can solve from here.
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  3. #3
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    Quote Originally Posted by wingless View Post
    \int_0^1 t \sin t (e^t + t e^t)~dt (the bounds of integration changes because of the differential dx -> dt)

    I guess you can solve from here.
    How do I integrate \int_0^1 t \sin t (e^t + t e^t)~dt? Thanks for helping!
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  4. #4
    Super Member wingless's Avatar
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    Quote Originally Posted by Tangera View Post
    How do I integrate \int_0^1 t \sin t (e^t + t e^t)~dt? Thanks for helping!
    \int t \sin t (e^t + t e^t) ~dt = \int t^2 \sin t e^t ~dt + \int t \sin t e^t~dt

    Both of them has the same idea, integration by parts. For \int t \sin t e^t~dt let u = t and dv = \sin t e^t~dt. You'll need to find the integral of \sin t e^t which you can find using another integration by parts.
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