area

ILoveBaseball

Find the area of the region bounded by: [tex]r= 6-2sin(\theta)[/tex]

here's what i did:

[tex] 6-2sin(\theta) = 0[/tex]
[tex] sin(\theta) = 1/3[/tex]

so the bounds are from arcsin(-1/3) to arcsin(1/3) right?

my integral:
[tex]\int_{-.339}^{.339} 1/2*(6-2sin(\theta))^2[/tex]

i get a answer of 0.6851040673*10^11, and it's wrong. all my steps seems to be correct, i cant figure out the problem.

marlon

What is the answer that you should have got ???

marlon

asrodan

[tex]r= 2sin(\theta)[/tex] is an ellipse so [tex]r= 6-2sin(\theta)[/tex] is just shifting and stretching it.

Therefore the bounds on [tex] \theta [/tex] are [tex] 0 \leq \theta \leq 2 \pi [/tex]

dextercioby

I agree.It's a shifted & stretched ellipse.Pay attention with the numbers...You can't get a big value for the area.It's ~100...

Daniel.

[itex] 38\pi [/itex] to be exact.

ILoveBaseball

can you explain it to me agian? i dont really understand it that well. are you saying if it's an ellipse, the bounds will always be from 0 ->2pi?

dextercioby

Yes,it's like for a circle,or for any closed curve enclosing the origin inside it...

Daniel.

ILoveBaseball

ah, i get it now. thank you