# Evaluate the line integral

1. Apr 29, 2015

### Calpalned

1. The problem statement, all variables and given/known data
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. $\int_C y^4 dx + 2xy^3 dy$, C is the ellipse $x^2 + 2y^2 = 2$.

2. Relevant equations
Change of variables: $\int \int_S f(x(u,v),y(u,v)) |{\frac {\partial(x,y)}{\partial (u,v)}}| du dv$

3. The attempt at a solution
How do I change the ellipse to a circle? Is there a way to determine u and v?

2. Apr 29, 2015

### Zondrina

Anyway, after parametrizing the ellipse, you should know what the limits on the integral are for $r$ and $\theta$ without very much thought.
While a change of variables $x = au$ and $y = bv$ would map the ellipse to a circle of radius $\sqrt{2}$, this is unnecessary and a bit of extra work since you still need to calculate the Jacobian.