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Math Help - triple integral ?

  1. #1
    n22
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    triple integral ?

    Hello,
    please advise..give suggestions.thanks.
    Is it bad to expand out (x+2y) first ?then integrate it ?can doing it this lead to getting the wrong answer??
    Here
    ∫∫∫(x+2y)dxdydz

    the first inner integral ranges from 0 to 1
    the next one goes from -2 to 0
    the last one goes from 0 to 3
    what is the best way of integrating this ??





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  2. #2
    MHF Contributor
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    Re: triple integral ?

    Yes expanding first is a valid move, and probably will make integrating the function easier as you won't have to use substitutions.
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  3. #3
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    Re: triple integral ?

    And, in fact, when you do that, the integral becomes
    \int_0^3 dz\left(\int_0^1 x^2dx\int_{-3}^0 dy+ 4\int_0^1 xdx\int_{-3}^0 y dy+ 4\int_0^1 dx\int_{-3}^0 y dy\right)

    Of course \int_a^b dx (or dy or dz) is just b- a.
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