Using the moment area method please solve for the slope at both A and B and the the deflection at C$.$ The slope at A should be $(3$qL$^3/128$EI$),$ the deflection at C should be $(5$qL$^4/768$EI$)$ and the slope at B should be $(7$qL$^3/384$EI$).$ When the known values for q and L are plugged in it should be$.$ A: $(3/8$EI$)$ & C: $(5/24$EI$)$ & B: $(7/24$EI$)($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 $B$