Consider the vector field $F=($:$y,x$:$)$ shown on the right.

a$.$ Compute the outward flux across the quarter circle $C$:$r(t)=($:$18cost,18sint$:$)$ for $0t\frac{}{2}.$

b$.$ Compute the outward flux across the quarter circle $C$ : $r(t)=($:$18cost,18sint$:$)$ for $\frac{}{2}t.$

c$.$ Explain why the flux across the quarter circle in the third quadrant equals the flux computed in part $($a$).$

d$.$ Explain why the flux across the quarter circle in the fourth quadrant equals the flux computed in part $($b$).$

e$.$ What is the outward flux across the full circle?

a$.$ Compute the outward flux across the quarter circle $C$:$r(t)=($:$18cost,18sint$:$)$ for $0t\frac{}{2}.$

The outward flux is $$