# Math Help - double integrals

1. ## double integrals

given that vector filed F= < 2x+ sin y, xcosy>, find integral F.dr where C is the arc y=1-x^2 from (0,1) to (1,0).

my working

integral F. dr = double integral curl F dxdy =0.

what is wrong with my workings?

i know that i can make use of F= grad f to solve this question..but im just wondering why my this method doesnt give me the correct answer.

2. To use Stock teorem curve must be closed and make a boundary to surface integral, in your case it is not.

3. i understand that to be a closed curve, it means to be something like a circle, where the curve starts and ends at the same point.

but what does it mean that it makes a boundary to surface integral?

thanks!