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Setting up double integral for polar coordinates and integrating

  1. Jul 14, 2011 #1
    Link:

    http://imageshack.us/photo/my-images/39/18463212.jpg/

    This is a very long problem so I drew it to make things simpler.

    Part a) tells me to set up a double integral in polar coordinates giving the total population of the city.

    I have the following:
    2π.....4
    ∫......∫ δ(r, θ) r dr dθ. Is this correct?
    π/2...1

    For part b) I was plugging in numbers, but I feel it can be both i) and ii). Can someone help me figure this out?

    For part c) all I would need to do is use what I find in part b) as the integrand for the double integral in part a).

    Thank you!
     
  2. jcsd
  3. Jul 15, 2011 #2
    If anyone can help me, I would be greatly appreciated.
     
  4. Jul 15, 2011 #3

    SammyS

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    The upper limit of integration for θ is wrong.
     
  5. Jul 15, 2011 #4
    How is it wrong? if you look at it from the side, it should be from pi to pi/2. along the x-axis it's 0 degrees.
     
  6. Jul 15, 2011 #5
    Shouldn't it be from pi/2 to 3pi/2?
     
  7. Jul 15, 2011 #6

    SammyS

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    It appears that Jaynte is correct.

    In which case you should be able to choose between i & ii for pat (b).
     
  8. Jul 15, 2011 #7

    SammyS

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    Yes: The population density, δ, decreases the farther you live from the shoreline.
     
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