$3.$ A board whose width changes as w$($x$)=2($Lx$)(0$ x L$),$ as shown is fixed on the left edge. Here L is the length ofthe board. The material has an area mass density $($per unit area$)$ of kg$/$m$2.$a$)$ What is the weight of the board? Derive it by integrating the weight of a differential element, dA located at x and that hasa width w$($x$)$ as shown.b$)$ What is the moment of the weight of the board about the yaxis? Derive it by integrating the moment applied by thedifferential element, dA$,$ located at distance x away from the fixed edge.c$)$ An additional distributed load, that is constant along the width but changes with distance as F$($x$,$ y$)=$ kx$2$N$/$m$2,$ is appliedon the board $($the gray surface in the figure is the force function$).$ What is the moment applied by this external load on the fixededge? Solve this using a similar approach as step $($b