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Help double integral over a region question

  1. Oct 29, 2009 #1
    I've tried this question with many different ways and i always got -11.576, but the autograder always marked it wrong. so hopefully i really did something wrong and you can teach me about it.

    find the double integral of -3*x*y - 3*y over the region bounded by x^2 + y^2 = 9, y = 3x, and y = 0.

    Thanks very much!
     
  2. jcsd
  3. Oct 30, 2009 #2

    tiny-tim

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    Hi kidzonety! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    The obvious way is to convert to polar coordinates (though of course you could also do it in x and y) …

    I expect you've already tried that, but anyway show us how you did it, and then we'll see what went wrong, and we'll know how to help! :smile:
     
  4. Oct 30, 2009 #3
    Okay.
    I just first converted the function to polar one which became -3*r3*cos(o)*sin(o) - 3*r2*sin(o) drdo
    and just double integrate this over 0 <= r <= 3, and arctan(3) <= o <= pi/2.
     
  5. Oct 30, 2009 #4

    tiny-tim

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    Hi kidzonety! :smile:

    (have a theta: θ and an integral: ∫ and a ≤ :wink:)
    ok (except it's 0 ≤ θ ≤ arctan(3)) … now split that into two integrals, ∫∫-3*r3*cosθ*sinθ drdθ and ∫∫-3*r2*sinθ drdθ,

    which are now just ∫-3*r3dr*∫cosθ*sinθdθ and ∫-3*r2dr∫sinθdθ :smile:
     
  6. Oct 30, 2009 #5

    hey tiny-tim,
    Ive found my mistake.
    Thanks very much for your suggestions and advice!
     
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