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Math Help - Calc 3 - Double Integrals in Polar Coordinates

  1. #1
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    Calc 3 - Double Integrals in Polar Coordinates

    Hi there,

    I'm absolutely drowning in my Calc 3 class and was hoping maybe someone here could explain things in terms that I understand. Naturally I've been pouring over my book and what-not, but there's one section that I just cannot seem to wrap my head around no matter how hard I try.

    Here are some examples of problems:
    1) Evaluate the following integral by changing to polar coordinates
    \int \int_{D} {x} {dA}
    where D is the interval in the first quadrant that lies between the circles:
    x^2 + y^2 = 100
    x^2 + y^2 = 10x

    2) Use a double integral to find the area of the region:
    One loop of the rose: r=9 \cos {3t}
    (the "t" should be a theta; can't figure out how to make it show correctly)

    3) Use polar coordinates to find the volume of the given solid:
    Above the cone
    z=\sqrt {x^2+y^2}
    And below the sphere
    x^2+y^2+z^2=13


    I don't expect anyone to solve these for me (in fact they are practice problems and I already have the answers) - I just want to know HOW to do them. I suspect the approaches to all three are very similar, but if I'm unwittingly asking too much here I would appreciate something like a link to a tutorial or something that could maybe help me.

    Thanks for your time; any and all help is greatly appreciated
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  2. #2
    A Plied Mathematician
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    What ideas have you had so far?
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  3. #3
    MHF Contributor

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    Do you know what "dA" is in polar coordinates? What values of \theta lie in the first quadrant? Have you drawn a picture?
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