1. ## Curve Integrals

"The integral I is defined by

I=∫F.dr where F(x,y)=(x-y),(xy)

And C is the triangle with vertices (0,0), (1,0) and (1,3) traversed anticlockwise.

Calculate the line integral directly"

2. I'd rather use Green's Theorem.
BUT if you wish to do this directly you need to figure out the three lines parametrically.

From (0,0) to (1,0)
you can let y=0, x=t where 0<t<1
note that dy=0, dx=dt

From (1,0) to (1,3)
you can let y=t, x=1 where 0<t<3
here dy=dt, dx=0

Finally you have
(1,3) to (0,0)
you can let y=3t, x=t BUT 1<t<0 since you are heading to (0,0)
then dy=3dt, dx=dt

3. The next part of the question is to verify using Green's Theorem. Thanks for that! I knew it involved parametric equations, just wasn't sure on how to set them up.