# Greens theorem-help setting up correct integral

## 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

## 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

$$\int$$$$\int$$4y-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

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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.

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?

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 $a>b, c>d$?