Using Green's Theorem to evaluate the line integral.

[Unart]

Homework Statement

Green's Theorem to evaluate the line following line integral, oriented clockwise.
∫xydx+(x^2+x)dy, where C is the path though points (-1,0);(1,0);(0,1)

Homework Equations

Geen's theorem: $∫F°DS=∫∫ \frac{F_2}{δx}-\frac{F_1}{δy}$

The Attempt at a Solution

What would I use for the bounds. I know it has to do with the triangle. But how would I find the bounds?

 

[HallsofIvy]

You've pretty much written it down yourself: the lower limit is clearly y= 0. The upper limits are those two other sides of the triangle: if x< 0, y= x+ 1, if x> 0, y= -x+1.
So you can divide this into two sets of integrals: for x from -1 to 1, y goes from 0 to x+ 1, for x from 0 to 1, y goes from 0 to 1- x.

 

[Unart]

Thanks... Halls. I wasn't sure what to do, but I understand now. It's like you've divided the triangle into 2 pieces.

 

[Unart]

And made both of the equations x+1 and 1-x satisfy their respective points... but I think the upper and lower bound of x+1 is -1 and 0 respectively since it goes from 0 to satisfy point (0,1) and -1 for (-1,0) and goes from the first point to the other.