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Homework Help: Double Intergral

  1. Feb 25, 2007 #1
    First attatchment is an integral I have been given.

    Using different values of k I have to find out what value the integral converges too.

    What I want to know is does this mean integrating the volume of circle with radius 1.

    Shown in formula in the second attachment, I have also arranged it using polar coordinates.

    And if that is right, I have found but only using mathcad that if k = 1/infinity the value converges to pi.

    Is that right, because how I suppose to integrate the function shown using fractions to k, surely this is too complex to do by hand.

    Cheers Ash
     

    Attached Files:

  2. jcsd
  3. Feb 25, 2007 #2
    And how do import pictures from mathcad into the post without having to make them attachments.

    Cheers
     
  4. Feb 26, 2007 #3

    HallsofIvy

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    Science Advisor

    A circle of radius 1 doesn't have a "volume"! What it means is that you are to integrate the given function over the interior of the circle.

    And k can't "equal 1 over infinity" because infinity is not a number. Do you mean k= 0?

    Yes, polar coordinates is the way to go here. You are aware, are you not, that [itex]sin^2(\theta)+ cos^2(\theta)= 1[/itex], so that x2+ y2= r2? That simplifies your integral a great deal!
     
  5. Feb 26, 2007 #4
    Yes sorry I meant area, not volume,

    and yes i know it simplifies, i was just asking whether I had interpreted the problem correctly.

    and yes by 1/infinity I did mean zero.

    I was meaning as k gets smaller it converges to pi.

    So is the function that i posted the right interpretation of the problem?

    Cheers Ash
     
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