Find the Area of the Interior


by mmmboh
Tags: area, greens theorem, integral, parametrize
mmmboh
mmmboh is offline
#1
Feb15-10, 02:32 PM
P: 408
Find a parametrization of the curve x2/3+y2/3=1 and use it to
compute the area of the interior.

What I did was y=(1-x2/3)3/2

I then integrated this function from 0 to 1 (using maple since it is a crazy integral) and got the answer to be 3/32 [tex]\pi[/tex].

However this is wrong, I probably wasn't suppose to do it the way I did anyway considering that the integral is so complicated.

So what should I do? I am learning Green's theroem right now if that helps, although I may have skipped ahead in it a bit I'm not sure.

Thanks.

Edit: Hm ok I have figured out what to do, the answer is 3/8 pi. How come my original answer is 1/4 of this though?
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tiny-tim
tiny-tim is offline
#2
Feb15-10, 04:15 PM
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P: 26,167
Hi mmmboh!
Quote Quote by mmmboh View Post
Find a parametrization of the curve x2/3+y2/3=1
They want you to use a parametrisation.

For example, if it were x2+y2=1, you'd use x = cosθ, y = sinθ.


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