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Double Integrals and circles - Confirmation Wanted

  1. Jan 30, 2006 #1
    Hey, my Q is:

    "Integrate f(x, y) = Sqrt(x^2 + y^2) over the region in the x-y plane bounded by the circles r = 1 and r = 4 in the upper half-plane".

    Well, I firstly sketched out the region I get as my area in the x-y plane. I deduced that the ranges for x and y are:

    0 <= x <= 4
    Sqrt[1 - x^2] <= y <= Sqrt[16 - x^2]

    1.) Is this right?
    2.) How do I then calculate the integral of f(x, y) over this region? I know I'm doing a double integral but I don't see how I can seperate my variables...

  2. jcsd
  3. Jan 30, 2006 #2


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    Homework Helper

    Have you covered polar coordinates?
  4. Jan 30, 2006 #3
    Hi, no unfortunately I haven't covered polar co-ordinates yet.

    mmm so yes I see that f(x, y) = r and now we have 2 circles with radii r = 4 and r = 1 respectively.

    Could you explain to me how to do this Q if that's ok? Thanks.
  5. Jan 30, 2006 #4
    Just think about it. from what pts are we integrating wrt the radius? Then, what angle to what angle are we integrating (wrt theta). drawing a picture is helpful.
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