Using the cross$-$section you designed in CPS #$7$ and a $E=1\mathrm{.}5({10}^6),$ determine the maximum deflection at the center of the beam with the integration method. Note: There will be two different equations from $0$ to $\frac{L}{2}$ and from $\frac{L}{2}$ to $L,$ you will be able to look at either part of the beam when integrating and still get the right answer. I would recommend $0$ to $\frac{L}{2}.$ For this calculation I will allow you to ignore self$-$weight.