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Math Help - Evaluating an integral by change of variables

  1. #1
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    Evaluating an integral by change of variables

    Q) Evaluate the integral

    <br /> <br />
\iint\limits_D (x - y)\,dA \\
    <br />
 D = \{(x,y)\lvert 0\leq x+y\leq 2, 0\leq xy \leq 1\}<br /> <br />


    A) My approach:
    u=x+y
    v=xy

    Found the Jacobian to be \frac{1}{2x-2y}

    Rewrote the whole thing to find the answer 1.


    Is the approach correct?
    Is my answer correct?
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  2. #2
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    Quote Originally Posted by keysar7 View Post
    Q) Evaluate the integral

    <br /> <br />
\iint\limits_D (x - y)\,dA \\
    <br />
D = \{(x,y)\lvert 0\leq x+y\leq 2, 0\leq xy \leq 1\}<br /> <br />


    A) My approach:
    u=x+y
    v=xy

    Found the Jacobian to be \frac{1}{2x-2y}

    Rewrote the whole thing to find the answer 1.


    Is the approach correct?
    Is my answer correct?
    Everything looks OK.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Everything looks OK.
    Thank a lot.
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