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Math Help - double integrals

  1. #1
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    double integrals

    Could someone go through this step step by step?
    I get stuck at part ii



    Thanks
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  2. #2
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    Quote Originally Posted by bille View Post
    Could someone go through this step step by step?
    I get stuck at part ii



    Thanks
    Assuming that you have done part (i), the essential next step is to draw a diagram of the domain D. That should enable you to describe D in terms of u and v, namely that D is enclosed by the lines u=1, u=e, v=0 and v=\pi. The change of variables formula then tells you that the integral is equal to

    . . . . . \displaystyle\int_1^e\int_0^\pi\frac{\sin v}{x^2}\,\frac{x^2}u\,dvdu.

    The " x^2"s conveniently cancel, and from then on the integral should be easy.
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  3. #3
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    Sorry, what is the change of variable formula?
    Thanks for our reply.
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  4. #4
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    Quote Originally Posted by bille View Post
    Sorry, what is the change of variable formula?
    The formula says that if you make a change of variables from (x,y) to (u,v), so that f(x,y) becomes g(u,v), then the integral \displaystyle\iint_Df(x,y)\,dxdy becomes \displaystyle\iint_Dg(u,v)\left|\frac{\partial(x,y  )}{\partial(u,v)}\right|dudv.

    See here for more on this topic. (But if you are being asked to do problems like this, then presumably it is expected that you already know this stuff.)
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