# Line integral with green's theorm

1. Dec 14, 2007

### damndamnboi

i would like to find the area bounded by the curve

(((x^2)/(a^2))+((y^2)/(b^2)))=xy/(c^2)

i used the substitution given x=(ar)cos(theta) and y=(ar)sin(theta)

i get :

(r^2cos^2(theta)+r^2sin^2(theta))^2=xy/(c^2)

thus r^4=xy/(c^2)
substituting x=(ar)cos(theta) and y=(ar)sin(theta) on the right hand side, i get
r^4=(r^2)(ab(cos<theta>)(sin<theta>)/c^2

then r^2=ab(cos<theta>)(sin<theta>)/c^2

then i used jacobian to transform dxdy to drd(theta):

i get abr(dr)(d(theta))

then i carried out the double integral
-- --
/ /
/ / abr(dr)(d(theta))
-- --

Last edited: Dec 14, 2007
2. Dec 14, 2007

image not working for me.

i'd recommend putting in a little bit of time to learn what you need to about latex to be able to post your problem. knowing latex is important if you intend on publishing research papers, anyway.

3. Dec 14, 2007

### damndamnboi

thx for telling me about the image not working, i have posted the question in typed form, please take a look. thx.

4. Dec 15, 2007

$$dxdy = drd\theta$$.

the correct relationship is

$$dxdy = rdrd\theta$$.

5. Dec 15, 2007

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=\frac{xy}{c^2} \smallskip \mbox{let} x=ar\cos\theta \mbox{and} y=ar\sin\theta \smallskip (r^2\cos^2\theta+r^2\sin^2\theta)^2=\frac{xy}{c^2}$$