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Integrating over a disk

  1. Oct 26, 2011 #1
    I'm taking a probability class where multivariate calculus was not a prerequisite, but some of it is coming up, I get the concept of, say integrating over a region, but get lost in some of the mechanics

    Here is the problem (I don't want a full solution):


    A point is uniformly distributed within the disk of radius 1. That is its density is
    [itex]
    f(x,y) = C \hspace{1cm} 0 \leq x^2 + y^2 \leq 1
    [/itex]
    Find the probability that its distance from the origin is less than x, 0 \leq x \leq 1

    I'm pretty sure I have to set up an integral that integrates over a disc of radius x to get the probability
    Something like this
    [itex]
    \int_A \int_B C \, dx \, dy
    [/itex]
    But I don't know what the intervals A and B are supposed to be.

    Can someone point me in the right direction? I get confused because my attempts end up with x being involved in the limit of integration, but x is the dummy variable, which doesn't seem right.
     
    Last edited: Oct 26, 2011
  2. jcsd
  3. Oct 26, 2011 #2

    Mark44

    Staff: Mentor

    Shouldn't the inequality be 0 <= x2 + y2 <= 1?
     
  4. Oct 26, 2011 #3
    Yes, sorry. 0 <= x^2 + y^2 <= 1

    I fixed it above.
     
  5. Oct 26, 2011 #4

    Mark44

    Staff: Mentor

    This would be a natural for polar form of a double integral.
     
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