The area of the region enclosed by a simple closed curve C will be _________.
1
\(\frac{1}{2} \int_c\left(\frac{1}{x} d y-\frac{1}{y} d x\right)\)
2
\(\frac{1}{2} \int_c(x d y-y d x)\)
3
\(\frac{1}{2} \int_c(y d x-x d y)\)
4
\(\frac{1}{2} \int_c\left(\frac{d x}{x}+\frac{d y}{y}\right)\)