Prove Integral_C y dx + x dy Depends on Endpoints of Curve C - Maya

[mayaitagaki]

I am soooo poor at this kind of proof problem...
Please help me out with this!

Show that

Integral_C y dx + x dy depends only on the endpoints of the arbitrary curve C.

(Hint: find a potential function f of the vector field <y, x> and use that to integrate
along a parametrization r(t) = <x(t), y(t)> of C with endpoints at t = a and t = b.)

I also attached a jpg file!

Thank you,
Maya

 

[lanedance]

have you tried the hint? finding a scalar potential should be reasonably staightforward