$($Chapter $15,$ Section $16\mathrm{.}5)$ A particle moves from $(1,1,0)$ to $(-1,1,-1)$ under the influence of the vector field F$\_($x$,$y$)=(2$xyz$,$x$^(2)$z$+2$yz$^(2),$x$^(2)$y$+2$y$^(2)$z$+$e$^($z$))($a$)$ Show that the integral is independent of the path followed by using the Fundamental Theorem of Line Integrals $($Theorem $16\mathrm{.}5\mathrm{.}1).($b$)$ Compute the integral i$.$ by transforming the integral to an ordinary single integral $($see Section $15\mathrm{.}3)$ ii$.$ using the Fundamental Theorem of Line Integrals.