Chapter 15.8, Problem 12ES

Use Stokes’s Theorem to evaluate ${\displaystyle \underset{C}{\oint }\text{F}.dr.}$

$\text{F(}x,y,z)=(z+\sin x)\text{i}+(x+y^2)\text{j+}(y+e^z\text{)k;}C$ is the intersection of the sphere $x^2+y^2+z^2=1$ and the cone $z=\sqrt{x^2+y^2}$ with counterclockwise orientation looking down the down the positive z-axis.