Green's Theorem and a triangle

[EV33]

Homework Statement

Use Green's Theorem to evaluate ∫F*dr.
(Check the orientation of the curve before you applying the theorem.)

F(x,y)=<y²cos(x), x²+2ysin(x)>

C is the triangle from (0,0) to (2,6) to (2,0) to (0,0)

*=dot product

Homework Equations

Green's Theorem

The Attempt at a Solution

-∫∫2x+2ycos(x)-2ycos(x) dydx= -∫∫$$_{D}$$ 2x dydx

D={0$$\leq$$y$$\leq$$3x, and 0$$\leq$$x$$\leq$$2)

I put the negative out front because the problem goes from point to point in a clockwise direction. Is this set up correct?
Thank you for your time.

 

[Dick]

Looks ok to me.