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Math Help - integral limits, i dont understand

  1. #1
    Newbie
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    integral limits, i dont understand

    heres a quick overview of my problem for a triple integral i have:

    (((_v where bracket is integral sign lol.

    where V is the region bounded by the planes x+y+z=a, a>0, x=0, z=0.

    my notes say the limits are 0<x<a ,a-x<y<a , a-(x-y)<z<0 for dzdydx.

    if i rearrange x+y+z=a i can never come up with the limits i have written down or have a clue how to... how do i get the limits! thanks so much.
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  2. #2
    Super Member Showcase_22's Avatar
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    a-(x-y)<z<0
    the z limits should be 0<z<a-x-y.

    Does your book say what you posted?

    EDIT: Also, can you post the question?
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  3. #3
    MHF Contributor Amer's Avatar
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    first you must know how to sketch the graph
    x+y+z=a
    to graph a curve like this first put x or y or z zero lats put z=0

    x+y=a now draw this
    integral limits, i dont understand-graph.jpg
    do the same thing set y to zero and draw z+x=a ...
    you will get
    integral limits, i dont understand-graph2.jpg
    now to determine the integral limits
    integral limits, i dont understand-graph3.jpg

    as you can see z values change from 0 to a-x-y this for z
    now after you determine limits for a variable now return to the x-y graph
    you can see that y values change from 0 to a-x
    integral limits, i dont understand-graph4.jpg
    and finally you can see that x values change from 0 to a
    thats all
    integral limits, i dont understand-graph5.jpg

    now
    \int_{0}^{a}\int_{0}^{a-x}\int_{0}^{a-y-z} dzdydx
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