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Math Help - Double Integral Problem

  1. #1
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    Double Integral Problem

    If ∫−1to3 f(x) dx = −3 and ∫−4to−2 g(x) dx = −2, what is the value of ∫∫D f(x)g(y) dA where D is the square: −1 ≤ x ≤ 3, −4 ≤ y ≤ −2?


    I am confused on where to start for this problem.

    BTW, -1to3, and -4to-2 are the integral bounds for their respected variables.

    Thanks!
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  2. #2
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    Your double integral is written as

    \displaystyle \int_{-1}^3{\int_{-4}^{-2}{f(x)\,g(y)\,dy}\,dx}

    \displaystyle = \int_{-1}^3{f(x)\,\int_{-4}^{-2}{g(y)\,dy}\,dx}

    \displaystyle = \int_{-1}^3{-2f(x)\,dx}

    \displaystyle = -2\int_{-1}^3{f(x)\,dx}

    \displaystyle = -2(-3)

    \displaystyle = 6.
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  3. #3
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    Ok great!

    They key I know understand is breaking the problem up, recognizing the integral bound and going from there.

    Thanks a lot!
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