Consider the following vector field F$($x$,$y$,$z$)=$Mi$+$Nj$+$Pk$.$

F$($x$,$y$,$z$)=$y$^(2)$zi$+2$xyzj$+$xy$^(2)$k

$($a$)$ Show that F is conservative.

curl F$=$

$($b$)$ Verify that the value of $\backslash$int$\_$C F$*$dr is the same for each parametric representation of C$.$

$($i$)$

C$\_(1)$:r$\_(1)($t$)=$ti$+2$tj$+6$tkt

$\backslash$int$\_($C$\_(1))$ F$*$dr$=,$x

$($ii$)$

C$\_(2)$:r$\_(2)(\backslash$theta $)=$sin$(\backslash$theta $)$i$+2$sin$(\backslash$theta $)$j$+6$sin$(\backslash$theta $)$ktheta pi $)/(2)$

$\backslash$int$\_($C$\_(2))$ F$*$dr$=$