$($adapted from Hibbeler ${10}^{th}$ ed$.$ prob$\mathrm{.}12-108)$

Establish variables that describe the reactions at the supports,

then use the integration technique to find equations for slope and

deflection in terms of the support reactions, as well as w$,$ L$,$ E$,$ and

I $($assume EI is constant$).$ Combine appropriate boundary and$/$or

continuity conditions with your slope and deflection equations to write $($in terms of $w,L,E,$ and I$)...$

a$.$ a formula for the moment reaction at support A$.$

b$.$ a formula for the maximum deflection of the beam.