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Math Help - integration

  1. #1
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    integration

    I need help setting the bounds of this equation
    Find the volume of the solid bounded by the planes x=0 y=0 z=0 and x+y+z=6
    thank you
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  2. #2
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    Hello, koalamath!

    Find the volume of the solid bounded by the planes: . x+y+z\:=\:6,\;x=0,\;y=0,\;z=0

    The solid is in the first octant, bounded by the plane x + y + z \:=\:6
    . . which has intercepts: (6,0,0), (0,6,0), (0,0,6).

    We have: . V \;=\;\int\int_A z\,dA . . . where A is the region in the x\text{-}y plane.

    That region looks like this:
    Code:
          | 
        6 * 
          |:*
          |:::* 
          |:::::* 
          |:::::::*
          |:::::::::*
        - + - - - - - * - - -
          |           6

    We see that y goes from 0 to 6-x

    And x goes from 0 to 6.


    Therefore: . V \;=\;\int^6_0\int^{6-x}_0 (6-x-y)\,dy\,dx

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  3. #3
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    Thank you so much
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  4. #4
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    Wait i get 6 as the answer and that's wrong
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  5. #5
    Math Engineering Student
    Krizalid's Avatar
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    Your integration skills or arithmetic are wrong 'cause the answer is 36.
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