QUESTION $3$

$($a$)$ Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}yds$ along $C,$ an upper half of a circle radius $2.$ Consider $C$ parameterized as $x(t)=2cost$ and $y(t)=2sint,$ for $0t.$

$(10$ marks$)$

$($b$)$ Find the directional derivatives for a function $\frac{O}{?}=sin(yz)ln(x^2)$ at the point $(2,3,)$ in the direction of the vector $A=2i2j-5k.$

$(15$ marks$)$