Consider the integral
\(\underset{c}{\overset{{}}{\mathop \int }}\,\left( 3x-y \right)dx+\left( x+5y \right)dy\)
The integral being calculated is taken in counter clockwise direction over the closed curve C that forms the boundary of the Region R shown in the figure. The line integral evaluates to:
1
12 + π
2
9 + π
3
12 + 2π
4
9 + 2π