Suppose \(C\) is the closed curve defined as the circle \(x^2+y^2=1\) with \(C\) oriented anti-clockwise. The value of the line integral
\[
\oint_C (x\,dy-y\,dx)
\]
is equal to ____.
Show Hint
A standard result:
\[
\boxed{
\oint_C(x\,dy-y\,dx)
=
2\times(\text{Area enclosed})
}
\]
For the unit circle,
\[
\boxed{
2\times\pi=2\pi.
}
\]