Let

F$($x$,$ y$,$ z$)=(7$ex sin$($y$))$i $+(7$ex cos$($y$))$j $+4$z$2$k$.$

Evaluate the integral

$$ C

F $$ ds$,$

where

c$($t$)=$

$4$

t

$,$ t$3,$ exp$($

t

$)$

$,$

$0$ t $1.$

$($Note that

exp$($u$)=$ eu$.)$

$$ C

F $$ ds $=$