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Double integration when switching to polar coordinates

  1. Nov 27, 2012 #1
    1. The problem statement, all variables and given/known data
    Take the double integration of
    http://webwork.usi.edu/webwork2_files/tmp/equations/08/1294e87299342c0ccfe2f8a97055da1.png
    when f(x)=sqrt(4x-x^2)


    2. Relevant equations
    x=rcos(theta)
    y=rsin(theta)


    3. The attempt at a solution
    I know I plug in the r*cos(theta) and r*sin(theta) for the x and y in the equation I am integrating, but other than that i can't remember how to switch the limits about which I integrate. After I substitute and simplify I get double integral of 1 dr dtheta. How do I change the limits of the integration to polar?
     
  2. jcsd
  3. Nov 27, 2012 #2

    SammyS

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    Sketch the region to be integrated over.

    Write the boundary as r equal to some function of θ, r = g(θ) .

    The element of area in polar coordinates is r∙dr∙dθ .
     
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