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Math Help - Integration help needed, thanks

  1. #1
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    Sep 2007
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    Integration help needed, thanks

    Hi all,

    I'm wondering if someone can point me in the right direction for integrating this integral...

    \int \sin{(\frac{x}{y})} dy

    I'm not sure where to start,

    thanks all.
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  2. #2
    Senior Member
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    Feb 2010
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    Let y = xu. Then it becomes x\int \sin(\frac1u)du which is known not to have an antiderivative amoung the elementary functions. Wolfram Alpha can give it to you with special functions though.
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  3. #3
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    If anyone could check through my working it would be great.

    Q. Evaluate the following double integral

     \int\int_R \sin{\frac{x}{y}} dA

    Where R is the region bounded by the y-axis, y = \pi, x = y^2

    Drawing a horizontal line throughout the region, we end up with...

     \int^{\pi}_0 \int^{y^2}_0 \sin{\frac{x}{y}} dxdy

    This turns through integration into

     \int^{\pi}_0 [ -y\cos{\frac{x}{y}}]^{y^2}_0 dy

    Subbing in values turns it into

     \int^{\pi}_0 [-y\cos{y} + y] dy

    Integration by parts turning into

     [\frac{y^2}{2} - \cos{y} - y\sin{u}]^{\pi}_0

    Giving

     \frac{\pi^2}{2} - \cos{\pi} - \pi\sin{\pi} + \cos{0}

    Am I right so far?

    Thanks.
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