$(1$ point$)$

Use Stokes' Theorem to evaluate $\_($M$)($grad$\backslash$times F$)*$dS where M is the hemisphere x$^(2)+$y$^(2)+$z$^(2)=4,$x$>=0,$ with the normal in the direction of the positive x

direction, and F$=($:x$^(7),0,$y$^(2)$:$).$

Begin by writing down the "standard" parametrization of delM as a function of the angle $\backslash$theta $($denoted by $"$t$"$ in your answer$)$

x$=$

$,$ y$=$

$,$ z$=$

$\backslash$int$\_($delM$)$ F$*$ds$=\backslash$int$\_0^(2\backslash$pi $)$ f$(\backslash$theta $)$d$\backslash$theta $,$ where

f$(\backslash$theta $)=$

$($use $"$t$"$ for theta$).$

The value of the integral is