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Homework Help: Using a triple integral to find volume

  1. Apr 22, 2008 #1
    I'm supposed to find the volume of a solid bound by co-ordinate planes x=0,y=0, z=0 & surface z=1-y-x^2 and am having a lot of difficulty doing so. f(x,y,z) is not given so I am assuming it is one. I figure I should then take the triple integral dzdydx. Then, I made a 2D sketch for the xy plane to determine limits of integration. I took the ∫dz from 0 to 1-y-x^2 then ∫dy from 0 to 1-x, then ∫dx from 0 to 1, but I keep getting a negative volume so I must be doing something wrong... Please help!
  2. jcsd
  3. Apr 23, 2008 #2


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    you want the volume under the surface f(x,y)=1-y-x^2 so find the limits in the x,y plane and compute the integral
    \int dx dy f(x,y)
  4. Apr 23, 2008 #3


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    And what did you see when you made a 2D sketch for the xy plane to determine the limits of integration? The plane z= 1- y- x^2 crosses the plane z= 0, when 0= 1- y- x2 or y= 1- x2. Together with with x= 0, y= 0, that is half of a parabola. For each x, y goes from 0 to 1- x2, not 1-x.
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