# Thread: Greens Theorem (Need Help)

1. ## Greens Theorem (Need Help)

Can someone show me step by step how to work this problem out please.

Let C be the triangle with vertices (0,0), (1,0), and (1,2). Find the following line integral by two methods, directly and using greens theorem.

2xy^2dx + yx^2dy

Thanks!!!

2. Per Green's Theorem:

The equation of the line from (0,0) to (1,2) is y=2x.

$f(x,y)=2xy^{2}, \;\ g(x,y)=x^{2}y$

$\int_{C}2xy^{2}dx+x^{2}ydy=\int\int\left[\frac{\partial}{\partial{x}}(x^{2}y)-\frac{\partial}{\partial{y}}(2xy^{2})\right]dA=\int_{0}^{1}\int_{0}^{2x}(-2xy)dydx$

Can you finish up?.

3. im lost.

When you start the problem you have to find P and Q right?

So I think that is P = 2xy^2 Q = yx^2

4. so than dQ/ dx = ? dp/dy = ?

From what you were showing me how does this relate to that