A beam $AB,$ with a sliding support at A and a roller support at $B,$ is subjected to a distributed load with a peak intensity $q_o$ as shown in figure below. Determine:

a$.$ The equation of the deflection curve for beam $AB$ using the integration method.

b$.$ The deflection of the beam at $A,{}_A,$ if the distributed load of peak intensity is $q_0=50l\frac{b}{f}t,$ the beam flexural rigidity is $EI=2000$ kip$-f{t}^2$ and the length of the beam is $10$ ft $.$

c$.$ The angle of rotation at $B,{}_B,$ for the same values of $q_o,$ EI and L as part b$.($positive CCW$)$

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