Could you show the work behind these methods? 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 $B$