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Math Help - Double Integral

  1. #1
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    Double Integral

    Let
    f be continuous on [0; 1] and let R be the triangular region with vertices (0; 0); (1; 0) and (0; 1). Show that


     \int\int_{R}f(X+Y)=\int_{0}^{1}uf(u)\, du



    Hi All,

    I got stuck with the above question. Basically I got LHS:
    \int\int_{R}f(X+Y)=\int_{0}^{1}\int_{0}^{1-x}f(x+y)\, dydx

    How do I continue from here?
    Last edited by ineedyourhelp; November 10th 2010 at 12:45 PM.
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  2. #2
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    Hi QF203 classmate. Use the change of variable method taught in Lesson 9. Haha. Use u=x+y, and v=y.
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  3. #3
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    Quote Originally Posted by metallicsatan View Post
    Hi QF203 classmate. Use the change of variable method taught in Lesson 9. Haha. Use u=x+y, and v=y.
    You will also need to compute the Jacobian so that \displaystyle dy\,dx is transformed to \displaystyle |J|\,du\,dv or \displaystyle |J|\,dv\,du (whichever is easier).
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  4. #4
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    Thanks for the help. I had a similar problem too.
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