Find the area of the region.

  • Thread starter rcmango
  • Start date
  • #1
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Homework Statement



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 [Broken]

Homework Equations



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

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.
 
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Answers and Replies

  • #2
Gib Z
Homework Helper
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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!
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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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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