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Bounds on a Trip Integral

  1. Nov 6, 2009 #1
    1. I need to find the region E bounded by the parabolic cylinders y=x^2, x=y^2 and the planes z=0 and z=x+y



    2. y=x^2, x=y^2, z=0, z=x+y



    3. I figured that I should let z vary between zero and x+y and then find x and y in terms of actual numbers? I'm not entirely sure. I've graphed it in Mathematica and I'm still horrifically confused. In general, if anyone could lend advice on finding bounds in general, but specifically for this problem
     
  2. jcsd
  3. Nov 6, 2009 #2

    HallsofIvy

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    It should be easy to see that [math]y= x^2[/math] and [math]x= y^2[/math], in the xy-plane, intersect at (0,0) and (1,1).
    You want [itex]\int \int (x+y- 0)dydx[/itex]. The limits of integration depend upon whether you want to integrate first with respect to x or y. If the "outer" integral is with respect to x, then x must vary from 0 to 1. On the "inside" integral, for each x y must vary from [itex]y= x^2[/itex] to [itex]y= \sqrt{x}[/itex].

    (It suddenly occures to me that by "trip integral" you meant "triple integral". As a triple integral that would be [itex]\int\int\int dzdydx[/itex] where z ranges form 0 to x+y.)
     
    Last edited: Nov 6, 2009
  4. Nov 6, 2009 #3
    I didn't include the function, because I want to try to solve that part on my own, but it's actually a triple integral, so I would be correct in having z vary from 0 to x+y if I were to integrate with respect to z first?
     
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