Consider $\vec{f} = (2x-y)\hat{i} - yz^2 \hat{j} -yz^2 \hat{k}$ where $S$ is the upper half of the surface of the sphere $x^2 +y^2 +z^2 = 1$ and C is its boundary
$Stoke's$ Theorem :Let $S$ be a piecewise smooth surface bounded by piecewise smooth simple curve $C$ and $\vec{f}(x,y,z)$ be a continous vector function which has continous first order partial derivatives in a region of space which contains $S$. Then $\int_C \vec{f} . d\vec{r} = \int \int_S curl \vec{f} . \hat{n} ds $
My Question is : I want to ask that what is C which is the boundary of the surface S