Let $F(x,y,z)=($:$x,y,z$:$)$ and let $C$ be the ellipse $4x^2+9y^2=1,z=0.$ Find the integral ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*Tds.($There are multiple ways to do this$-$choose the one you want$).$

Let $F(x,y,z)=($:$y,-x,z-x$:$)$ and let the surface $S$ be the upper half$-$ellipsoid $4x^2+4y^2+9z^2=1,z0.$ Use Stokes' Theorem to evaluate the following by rewriting it as a line integral.

${}_S$curl$(F)*dS$