Greens theorem-help setting up correct integral

[hils0005]

Homework Statement

Use Green Theorem to calculate \oint\widehat{}F \bullet d\widehat{}r where C is the closed triangular curve oriented counterclockwise with verticies P1(0,5), P2(0,2) and P3(3,5). vectorF(x,y)= xy^2 i + 4xy j

Homework Equations

The Attempt at a Solution

I first took the partial of F2 with respect to x = 4y
partial of F1 with respect to y = 2xy

\int\int4y-2xy dA

I am not sure of what limits to use:
because it is oriented counter clockwise:
y-2\leq x \leq 0
5 \leq y \leq 2

 

[jeffreydk]

It looks fine except I would check your order of limits--it should be entering at x=0 and leaving at x=y-2 and it's backwards for y too--maybe that was just a mistake when you wrote it.

 

[hils0005]

that is how I did the problem initially however, the problem says it is in the counterclockwise direction which I would think y goes from 5 to 2, and x from 0 to y-2.
(which is only half of what I did)

Can anyone explain this?

 

[jeffreydk]

When you integrate a region, you do so on an interval x\in [a,b],y\in [c,d]. Does the integral make sense if a>b, c>d?