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Double Integrals -

  1. Jan 30, 2006 #1
    Double Integrals - Please Help!

    Hi, I have a question and it asks me to evaluate the volume generated by the area bounded by y = x^3 and y = x^(1/3) and the function z = x^2.y

    I'm just having a few problems with setting up the ranges of my variables x and y. I drew a sketch of the area in the x-y plane but I'm not sure what my ranges should be. My guess is: 0 <= x <= 1 and 0 <= y <= [x^(1/3) - x^3].

    Help appreciated.
     
  2. jcsd
  3. Jan 30, 2006 #2
    "Hi, I have a question and it asks me to evaluate the volume generated by the area bounded by y = x^3 and y = x^(1/3) and the function z = x^2.y"

    To do dbl int's always choose one of the variables to put definite boundaries on (put them on the outer-most int), then put limits on the second int in terms of the first. You know that the graphs intersect at (0,0) and (1,1), so I'd suggest using 0 and 1 as the bounds of x, then choose y = x^3 and y = x^1/3 for the bounds on y. Then, integrate!
     
    Last edited: Jan 30, 2006
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