Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Iterated Integrals bounded by curves

  1. Sep 17, 2007 #1
    Evaluate [tex]\int[/tex][tex]\int_{Q}\left(1 - x^{3}\right)y^{2} dA[/tex] where Q is the region bounded by y=x^2 and x = y^2

    So I have drew the graphs of y=x^2 and x=y^2 and found that they intersect at (0,0) and (1,1). Now I am confused what to replace Q with, but I think it should be this: please tell me if I am incorrect in my selection.

    [tex]\int^{1}_{0}[/tex][tex]\int_{\sqrt{y}}^{y^{2}}\left(1 - x^{3}\right)y^{2} dx dy[/tex]

    or should I be integrating w.r.t y first? also have I mixed up the y^2 and the sqrt(y) in the limit of integration?
  2. jcsd
  3. Sep 17, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    dxdy is correct, but sqrt(y) > y^2.
  4. Sep 17, 2007 #3
    how would i know this for future reference, i am having serious trouble with the limit of integration part.
  5. Sep 17, 2007 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Well, it's clear that either [itex]\sqrt{y} < y^2[/itex] for every y in that interval, or [itex]y^2 < \sqrt{y}[/itex] for every y in that interval, correct?

    So, if you try one actual value of y in that interval...

    A little algebra would solved it too: what happens if you manipulate that inequality to put all of the y's on the same side?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook