$(2)$ Find the work done by the vector field $F=($:$x^2+y,cos(y)+x,2z$:$)$ in moving a particle around the curve $C$ parameterized by $r(t)=($:$4-3^t,-2+2t,t$:$),0t1.($Your final answer may look nasty. Leave any trig values.$)(20$ pts $)$