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Double integral finding the area

  1. Apr 8, 2012 #1
    1. The problem statement, all variables and given/known data
    Use a double integral to find the area of the region bounded by the curve r= 1+sin(theta)?


    2. Relevant equations



    3. The attempt at a solution I can't figure out what theta is intregrated from. I've tried from -(pi)/2 -> +(pi)/2 and that doesnt work. I've also tried from 0-> 2(pi) and that doesnt work. I have no clue what im supposed to integrate theta to. I would really appreciate some help with this.
     
  2. jcsd
  3. Apr 8, 2012 #2

    SammyS

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    Have you done a polar plot?

    0 → 2π should give the right answer.

    What does your integral look like ?
     
  4. Apr 8, 2012 #3
    i put a picture up
     

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  5. Apr 8, 2012 #4

    SammyS

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    Your integral looks good:
    [itex]\displaystyle \int_0^{2\pi}\int_0^{1+\sin(\theta)}r\,dr\,d\theta[/itex]​

    What do you get for tour final answer?
     
  6. Apr 9, 2012 #5
    I get (3(pi) + 2)/2
     
  7. Apr 9, 2012 #6

    SammyS

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    Where does the " + 2 " come from ... as in
    (3(π) + 2)/2​
    ?

    What do you get upon integration w.r.t. r ?
     
  8. Apr 9, 2012 #7
    Oh I see what ive been doing now. When I evaluated theta at 0 I was getting -2. I forgot to multiply this by 1/2 which would have given me 3(pi)(-2+2)/2 or 3(pi)/2 for my final answer. Thank you so much for all of your help I was stuck on that problem for awhile. :smile:
     
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