For the beam and loading shown, integrate the load distribution to determine $($a$)$ the equation of the elastic curve, $($b$)$ the deflection at the left end of the beam, and $(c)$ the support reactions $B_y$ and $M_B.$ Assume that $EI$ is constant for the beam. Let $w_0=8k\frac{N}{m},L=4\mathrm{.}5m,E=175$GPa, and $I=150{10}^{6}m{m}^4.$