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Math Help - Multiple Integration

  1. #1
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    Multiple Integration

    Consider the rectangles
    B1 defined by 0< x <=1, 0<=y<=1
    B2 defined by 1<=x<=2, -1<=y<=1
    and the function
    f(x,y) = { 2x -y if x< 1
    { x^2 + y if x>=1
    Compute integral (B1 U B2) of f(x,y)dxdy
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Decompose:

    \displaystyle\iint_{B_1\cup B_2}f(x,y)dxdy=\displaystyle\iint_{B_1}(2x-y)dxdy+\displaystyle\iint_{B_2}(x^2+y)dxdy

    Regards.

    Fernando Revilla
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  3. #3
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    Start by drawing the two sets on a graph. It should be easy to see that B_1 and B_2 overlap only on the boundaries so the integral over both is just the sum of the integrals over each, as Fernando Revilla says.
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    B_1 and B_2 overlap only on the boundaries so the integral over both is just the sum of the integrals over each, as Fernando Revilla says.
    Of course is important your comennt ( \mu (B_1\cap B_2)=0 ) .

    Regards.

    Fernando Revilla
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