A flat semicircular gate AB$,$

articulated at B$,$ it is supported by the force

horizontal FA applied to A$.$ If y$=$rsin$($theta$)$ and

h $=$ H $-$ y

a$)$ By direct integration, find a

expression for the resultant force

b$)$ By direct integration, find a

expression for the force FA$.$

c$)$ Determine FR and FA for: $=8$m$,=$

$3$m$,$ density $=998$kg$/$m$^3$