D$7\mathrm{.}4.($a$)$ Evaluate the closed line integral of H about the rectangular path P$1(2,3,4)$ to P$2(4,3,4)$ to P$3(4,3,1)$ to P$4(2,3,1)$ to P$1,$ given H $=3$zax $2$x$3$az A$/$m$.($b$)$ Determine the quotient of the closed line integral and the area enclosed by the path as an approximation to $($ H$)$y$.($c$)$ Determine $($ H$)$y at the center of the area.

Ans. $($a$)354$ A; $($b$)59$ A$/$m$2$; $($c$)57$ A$/$m$2$