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Find the area of the region.

  1. Feb 14, 2007 #1
    1. The problem statement, all variables and given/known data

    find the area of the region bounded by r = 3 + 2sin(theta)

    heres a pic of the intended equations i have so far: http://img263.imageshack.us/img263/8804/untitledpk1.jpg

    2. Relevant equations

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

    3. The attempt at a solution

    2 * 1/2 integral (3 + 2sin(theta))^2 d(theta

    this is as far as i have gotten with this, i am not good with integrals, can someone help me with the rest of this please. thanks.
  2. jcsd
  3. Feb 14, 2007 #2

    Gib Z

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    Homework Helper

    ok Well basically you need help with this integral:

    [tex]\int^b_a (3 + 2\sin \theta)^2 d\theta[/tex].

    Expand the binomial. (I'm going to ignore the bounds for now, account for them later for me please :P)

    [tex]\int 9 + 12\sin\theta + 4\sin^2 \theta d\theta[/tex].

    Split the integral up. the first 2 parts are very easy, you should get this.

    [tex]9\theta - 12\cos\theta + 4\int \sin^2\theta d\theta[/tex].

    We know that [tex]\sin^2 \theta = \frac { 1-\cos {2\theta}}{2}[/tex]. Just sub that in, take out the factor of 1/2, split it up again, easy work. GOGOGO!
  4. Feb 14, 2007 #3


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    Staff Emeritus
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    Becareful when you are doing the part Gib Z did NOT do- determine the limits of integration. What values of [itex]\theta[/itex] will take you exactly once around the boundary?
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