I really am confused on how to solve this problem especially with regards to the first method, superposition and Castiglianos theorem. Can someone please help me solve for all the values. The answers I've recieved only solve for angle about B A simply supported beam ACB supports a uniform load of

intensity $q$ on the left half of the span $($L$)$ as shown in the

figure. Find deflection at $C$ and slope of the beam at A and $B$

using the following methods discussed in class

$($a$)$ Integration of beam bending moment

$($b$)$ Method of superposition

$($c$)$ Moment area method

$($d$)$ Combination of Modified Castigliano's theorem $($differentiation under the integral sign$)$ and fictitious

method

Briefly explain each method before presenting the solution.

Take $q=2K\frac{N}{m},L=2m$ and tabulate your results $-$ deflection at $C,$ slopes at A and $B$