Greens Theorem (Need Help)

**winterjm** · December 10th 2007, 03:52 PM

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!!!

**galactus** · December 10th 2007, 04:18 PM

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?.

**winterjm** · December 10th 2007, 04:31 PM

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

**winterjm** · December 10th 2007, 04:35 PM

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

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

Thread: Greens Theorem (Need Help)

LinkBack

Thread Tools

Display

Greens Theorem (Need Help)

Similar Math Help Forum Discussions

Greens Theorem

Greens theorem

Greens Theorem

help with greens theorem

Greens Theorem Help

Search Tags