Evaluate $o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}(2y-e^{sin(x)})dx+(6x+\sqrt[\phantom{2}]{y^4+1})dy,$ where $C$ is the circle $x^2+y^2=16.$

Solution

The region $D$ bounded by $C$ is the disk $x^2+y^{2}16,$ so let's change to polar coordinates after applying Green's theorem.