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Homework Help: Double integral in polar form: how do you find the boundaries?

  1. Mar 24, 2009 #1
    Hi I need to use a double integral to find the area of the region bounded by:

    r = 3 + 3sinQ where Q = theta.

    I know the bounds of the inner integral are from 0 to 3 + 3sinQ.

    However, I do not know how to determine the bounds of the outer integral.

    Any help would be greatly appreciated.
  2. jcsd
  3. Mar 24, 2009 #2
    The outer integral is just a typical single-variable polar integral. Play with the equation to figure out when the behavior of r begins to repeat itself as theta varies, paying particular attention to the periodic nature of sine. Perhaps a polar graph might help.
    Last edited: Mar 24, 2009
  4. Mar 24, 2009 #3
    Ok, well I know that once theta = 2pi, the behavior of of sinQ will repeat itself. Should I then plug in 2pi to the equation and work with that?

    I know the value of sinQ becomes zero again at pi. Does this mean the outer boundary is from 0 to pi?
  5. Mar 24, 2009 #4


    Staff: Mentor

    0 to pi, although you can exploit the symmetry of the figure by doubling the value you get integrating from 0 to pi/2.
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