Consider the beam with the loading shown. Assume the modulus of the material is $E=200$GPa and the moment of inertia is $I=6\mathrm{.}5({10}^{-5})m^4.$ Include final answers in the space indicated above, and be sure to show your work below for full credit.

$($a$)$ Find the slope at $B{}_B$ using the method of integration

$($b$)$ Find the deflection at $B{v}_B$ using the method of integration

$($c$)$ Consider if you had used the method of superposition to solve for the slope and displacement. Draw the beam configurations that you would use to complete the problem using the method of superposition $($the beams that you would "break up$"$ the original beam into$).$