Finding the area enclosed by r=3sin theta

  1. 1. The problem statement, all variables and given/known data

    Find the area enclosed inside r=3 sin (theta)

    2. Relevant equations

    integral?


    3. The attempt at a solution

    basically, I took [tex]\int3sin\Theta[/tex] from 0 to 2pi, then pulled the 3 out to get

    [tex]3\int sin\Theta[/tex] from 0 to 2pi and then

    [tex]3[-cos(\Theta)][/tex] evaluated from 0 to 2pi.

    that seems too easy. what am I missing?
     
    Last edited: Dec 15, 2008
  2. jcsd
  3. Dick

    Dick 25,852
    Science Advisor
    Homework Helper

    Who said everything has to be super hard? But if you work that out, you'll get 0 for the area. Is that right? It might help to draw a picture. And, hey, area in polar coordinates isn't the integral of r dtheta, is it? Would you look up the right formula for area?
     
    Last edited: Dec 15, 2008
  4. ah. that's what it was. I forgot about the formula for area. : (

    Thanks!
     
  5. HallsofIvy

    HallsofIvy 40,533
    Staff Emeritus
    Science Advisor

    Well, actually, Dick, area in polar coordinates is r dtheta! You didn't say quite what you meant to, did you?

     
  6. Dick

    Dick 25,852
    Science Advisor
    Homework Helper

    Are you SURE?
     
  7. Dick

    Dick 25,852
    Science Advisor
    Homework Helper

    The integral of r*dtheta*dr is the area. Not the integral of r*dtheta. I missed it at my first reading as well.
     
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