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Homework Help: Am I Doing This Area Problem Correctly?

  1. Sep 25, 2010 #1
    Hi there. The book doesn't have an answer in the back for this problem, so I wanted to know if I was setting everything up correctly.

    I need to find the area enclosed by r=1-sin(theta) but outside r=1. This is polar by the way. So a nice simple cardioid and circle. I decided to only do half and then double it, because of the symmetry.

    Here is the integral I got.
    [tex]
    2*\frac{1}{2}[\int_{\frac{-\pi}{2}}^{0}{(1-sin(\theta))^{2} d\theta} - \int_{\frac{-\pi}{2}}^{0}{(1)} d\theta}]
    [/tex]

    My answer was [tex]\frac{5\pi}{2}+\frac{9}{2}[/tex]. I'm fine with integrating, I'm just wondering if I set it up correctly.
     
    Last edited: Sep 25, 2010
  2. jcsd
  3. Sep 25, 2010 #2
    I am not that good at calculus,but perhaps if you could send me the complete question i might be able to help. Ezim.
     
  4. Sep 25, 2010 #3
    That is the complete question. Find the area enclosed by r=1-sin(theta) but outside r=1.
     
  5. Sep 25, 2010 #4
    you mean there is no diagram or figure?
     
  6. Sep 25, 2010 #5
    Nothing is given. I just drew a quick sketch and checked it on wolfram alpha.
     
  7. Sep 25, 2010 #6

    vela

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    You set-up looks fine, but your final result isn't correct. Check your work.
     
  8. Sep 25, 2010 #7
    Oh...5/2 + pi/4 I guess.
     
  9. Sep 25, 2010 #8

    vela

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    I get 2+pi/4.
     
  10. Sep 25, 2010 #9
    ...This is getting really silly really fast. Well we established that it's just an algebra issue. I'll work it out later. Thanks.
     
    Last edited: Sep 25, 2010
  11. Sep 26, 2010 #10
    yes. I solved it with double integral and I got 2+pi/4.
     
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