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Evaluate the following double integral

  1. May 18, 2005 #1
    Just had an exam and I had to evaluate the following double integral, with limited success :mad:

    [tex] \int_0^1 \int_0^{\pi} y\sin(xy) {dy} {dx}[/tex]

    I managed to compute the first integral, that was ok, using parts. But trying to integrate that with respect to dx just yielded a whole lot of trouble. Could someone have a skim over this and see if its do-able using elementary calculus procedures {I say elementary, but you know what I mean}.

  2. jcsd
  3. May 18, 2005 #2
    I would interchange the order of integration and integrate y Sin(x y) with respect to x to get -Cos(x y). Should be easy from here.
  4. May 18, 2005 #3
    Rotation of variables was not covered at all... So say you weren't armed with that tool, what then? (not a cop out, honestly)
    Last edited: May 18, 2005
  5. May 18, 2005 #4


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    Part integration wrt "y" and then integrate the result wrt "x",what else...?

  6. May 18, 2005 #5
    The second integration w.r.t x wouldnt work for me.... Right im going to write down what I've done.

    For the first inner integration, i have as follows:

    [tex] \int_0^{\pi} y\cdot \sin(xy) dy = -\frac{\pi}{x}\cos({\pi x}) + \frac{1}{x^2} \cdot \sin({\pi x}) [/tex]

    I have tried with an abundance of attempts to evaluate all that as an integral with respect to x and I go nowhere conclusive, and its really starting to irritate me. Man, i suck at this.

    Any hints or tips...please!! :confused:
    Last edited: May 18, 2005
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