Q$8(10$ points$)$

We define the average of $f$ on $c$ to be:

$A(f,c)=\frac{{\displaystyle \underset{c}{\overset{\phantom{}}{}}}fds}{{\displaystyle \underset{c}{\overset{\phantom{}}{}}}1ds}$

Calculate the average of

$f(x,y,z)=yonc(t)=(t^2,t,3)$

for $0t1.$