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Double Integral

  1. Oct 15, 2009 #1
    I need to find the area between the parabolas x=y^2 and x=2y-y^2, I know I need to use a double integral but am having difficulty finding the limits. Can anyone help please?
  2. jcsd
  3. Oct 15, 2009 #2


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    Hi Juggler123! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    No, for an area you'll only need a single integral …

    divide the area into strips of width dy, find the area of each strip, and integrate over y. :wink:
  4. Oct 15, 2009 #3


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    Well, you certainly could use a double integral to find area!

    The double integral
    [itex]\int_{x=a}^b \int_{y= f(x)}^{g(x)} 1 dy dx[/itex]
    has a very simple first integral of f(x)- g(x) so that the second integral is
    [itex]\int_{x=a}^b f(x)- g(x) dx[/itex]
    and that is the integral for area between the curves that tiny-tim is referring to.

    So, for your problem, first, determine for what values of x the graphs intersect. That will be your limits of integration a and b for the "outer" integral (a being the smaller, b the larger, of course). The decide which of the graphs is higher inside that interval. That will be f(x) and g(x), the limits of integration for the "inner" integral.
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