$$\int_D (x-y)\mathrm{d}x+y\mathrm{d}y$$ where $D: y=\sin x, x \in [0,\pi]$
I have no idea how to solve this, I barely did some line integrals of 1st kind if that's the correct english translation but for this one, I am not sure if i just do it the same way with the figure then parametrics then to calculate, and it'd help if I could get this as an example.
Since y= sin(x), dy= cos(x)dx.
(x- y)dx+ ydy= (x- sin(x))dx- sin(x)cos(x)dx= (x- sin(x)- sin(x)cos(x))dx
So the integral is $\int_0^\pi (x- sin(x)- sin(x)cos(x))dx$. That's easy to integrate.