# Thread: Green's Formula, polar co-ordinates

1. ## Green's Formula, polar co-ordinates

where
C is the ellipse x^2/a^2 + y^2/b^2 = 1
a,b>0

So basically I get upto II(-2)dxdy, with the elipse as limits, then converting to polar co-ordinates i'm unsure on the limits, but I have a vague idea it is sqrt(ab), can anyone confirm this? Would be appreciated, also can anyone tell me the best way be able to post all the different mathematical symbols

2. Let $\displaystyle \bold{F}(x,y) = (M(x,y),N(x,y))$ where $\displaystyle M(x,y) = x+y$ and $\displaystyle N(x,y) = x - y$.

Green's theorem says $\displaystyle \oint_C \bold{F} = \iint_D \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} = \iint_D (1 - 1) = 0$

However, if you had $\displaystyle \bold{F}(x,y) = (N(x,y),M(x,y))$ then:
$\displaystyle \oint_C F = \iint_D 2 = 2\text{area}(D) = 2\pi ab$

Because the area of the ellipse $\displaystyle D$ is given by $\displaystyle \pi ab$.

3. Where you have N(x,y)= x-y, should it not be = y-x

as there was a "-" in the original formula?

4. Originally Posted by pkr
Where you have N(x,y)= x-y, should it not be = y-x

as there was a "-" in the original formula?
Yes, I copied down your problem in correctly.
However, all the steps necessary to solve it are still there.
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