PROBLEM: For the shaded area bounded by the two lines and a parabola, calculate the following:

a$.$ Area bounded by the region

b$.$ First moment of the shaded area with respect to the $x-$axis

c$.$ First moment of the shaded area with respect to the $y-$axis

d$.$ Centroid $(\stackrel{}{x}\frac{,}{b}ar(y))$

e$.$ Moment of Inertia $($MOI$)$ about the $y-$axis using vertical strips

f$.$ Moment of Inertia $($MOI$)$ about the x$-$axis using horizontal strips

g$.$ Polar Moment of Inertia $($MOI$)$

h$.$ Radius of gyration about $x-,y-,$ and $z-$axis

i$.$ MOI about the centroidal $y-$axis

j$.$ MOI about the centroidal $y=-6$