$[$Problems$]1.$ Let F$($x$,$y$,$z$)=$ sin$($x$2)$i$+$xzj$+$z$2$k$.$ Evaluate C F$$dr around the curve C of the intersection of the cylinder x$2+$ y$2=4$ with the surface z $=$ x$2$ in the counterclockwise direction as viewed from the top of the z$-$axis. Let C be the curve of intersection of the cylinder x$2+$ y$2=4$ and the surface z $=$ x$2,$ oriented counterclockwise as viewed from above. We are asked to evaluate the line integral: $$ F $$d$$r$.$