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Area and Volume integral using polar coordinates

  1. Apr 30, 2012 #1

    I'm working on area and volume integrals. I was wondering, when you convert to do the integral in polar, cylindrical or spherical co-ordinates, is there a standard set of limits for the theta variable in each case?

    for example from 0 -pi for polar, 0-2pi for cylindrical?

    If not how do you set the limits?

  2. jcsd
  3. Apr 30, 2012 #2

    It all depends, of course, on the area to be integrated over. If, for example, you want to calculate the area of the

    upper semicircle [itex]x^2+y^2=R^2\,,\,\,y\geq 0[/itex] , then upon passing to polar co. you'll have [itex]0\leq \theta\leq \pi[/itex] .

    Over other areas you might have have different ranges.

  4. Apr 30, 2012 #3
    I see, Thankyou!
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