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Finding area in polar coordinates

  1. Feb 28, 2007 #1
    1. The problem statement, all variables and given/known data
    "Find the area of the region described: The region that is enclosed by the rose r=4cos3[theta]"


    2. Relevant equations

    A= [integral] (1/2)r^2 d[theta]

    3. The attempt at a solution

    I'll use Q as [theta]..

    I'm not really sure, but I set up (1/2) [integral] (16(cos^2)3Q) dQ

    .. then I thought we were supposed to use the identity (cos^2)Q = (1/2)(1+cos2Q), but every time I substitute this in and integrate, I get 8[pi] instead of 4[pi], the correct answer. What am I doing wrong?

    Thank you so much :]
     
    Last edited: Feb 28, 2007
  2. jcsd
  3. Feb 28, 2007 #2
    I get 8pi as well.
     
  4. Feb 28, 2007 #3
    hmmm, I asked someone else and they got 8pi too...


    Well I had one more question... if I were finding the area between
    r = sqrt[cos2(theta)] and
    r = 2cos(theta)

    do I basically do the same thing as finding the area between two regular curves? Each time I try it, I come up with zeros and I feel like that cant be right :[
     
  5. Mar 1, 2007 #4
    That's a really weird graph intersection. Where did you get that question from?
     
  6. Mar 1, 2007 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You don't say anything about what limits of integration you used. [itex]\theta[/itex] going from 0 to what traces that figure exactly once?
     
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