Question $1.(10+5$ points$)$

Consider the vector field $F(x,y,z)=(2x{y}^{2}z,2x^{2}yz,x^2{y}^2)$ and the curve

$C$ given $byr(t)=(sint,sintcost,cost),$tin$[\frac{}{4},\frac{3}{4}].$

Calculate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*drin$ two ways:

$(a)$ Directly, using the definition $of$ the line integral.

$(b)By$ evaluating the potential function $ofF$ and using the Funda$-$

mental Theorem for Line Integrals.