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Thread: Evaluating an integral by change of variables

  1. #1
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    Evaluating an integral by change of variables

    Q) Evaluate the integral

    $\displaystyle

    \iint\limits_D (x - y)\,dA \\$
    $\displaystyle
    D = \{(x,y)\lvert 0\leq x+y\leq 2, 0\leq xy \leq 1\}

    $


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

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

    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

    $\displaystyle

    \iint\limits_D (x - y)\,dA \\$
    $\displaystyle
    D = \{(x,y)\lvert 0\leq x+y\leq 2, 0\leq xy \leq 1\}

    $


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

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

    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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