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Homework Help: Triple Integrals

  1. Apr 10, 2005 #1
    [tex] \int \int \int_{G} (xy + xz) dx dy dz [/tex]
    G bounded by z=x, z= 2-x, and z = y^2

    solving the first 2 i get x =1

    equating y^2 = z =x and y^2 = 2-x
    so x can go from 1 to 2?
    not sure how to proceed for the y part, however..

    please helppppp
  2. jcsd
  3. Apr 10, 2005 #2
    so far i got the x lower boun to be 1 and upper boun to be 2

    i (think) that the z lower bound is zero and upper bound is y^2

    also the y lower boun would be root x and upper bound would be root (2-x)

    is this correct??
    Integrating would be a real bugger in this case

    please help!
  4. Apr 10, 2005 #3
    Try integrating dx first, with z constant. I've attached a graph to help you figure out the limits. Set your constraints in terms of x= and y=

    http://www.public.asu.edu/~hyousif/prob2.JPG" [Broken]

    The thin slant is z=2-x, the plane is z=x and the parabola is obviously z=y^2
    Last edited by a moderator: May 2, 2017
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