The cross$-$section is bounded by the z$-$axis and the parabola y$($z$),$ whose equation is given in the figure.

a$)$ Determine in symbolic form the moment of stiffness of the cross$-$section in the y$-$axis relation $I_y=I_y($b$,$ h$).$

b$)$ Determine in symbolic form the distance of the center of gravity from the z$-$axis e$($h$).$

c$)$ Determine in symbolic form the moment of stiffness of the cross$-$section in the z$-$axis $I_{}=I_{}(b,h)$ in relation to the center of gravity axis $.$

Partial answer: $I_y=\frac{h{b}^3}{30}$