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Finding the bounds of a double integral when told to find the area of one rose petal.

  1. Aug 4, 2009 #1
    Example:
    Use a double integral to find the area of the region:
    One loop of the rose r = Cos[3 theta]

    Finding the bounds of r is easy, 0 to Cos[3x]. However, I usually get the bounds of theta wrong. How do I find the bounds of theta without using a graphing calculator and guessing. The only method I currently know of is to solve Cos[3 theta]=0, but that gives me unnecessary solutions, like Pi/2 when the bounds really are -Pi/6 to Pi/6.
     
  2. jcsd
  3. Aug 5, 2009 #2

    tiny-tim

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    Hi jinksys! :smile:

    (have a pi: π and a theta: θ :wink:)
    That method is right!

    Cos3θ = 0 gives you ±π/6, ±3π/6 (=±π/2), and ±5π/6 …

    so just chose any two adjacent :wink: ones,

    such as {±π/6}, or {π/6,π/2} :smile:
     
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