For the beam and loading shown, determine

$($a$)$ the equation of the elastic curve for portion $AB$ of the beam,

$($b$)$ the slope at $A,$

$($c$)$ the slope at $B.$

Step $1$: Draw FBD and find reactions at A and $B$

Step $2$: Derive formula for Moment $M(x)$ between A and $M(x)EIEI\frac{1}{}=EI\frac{d^{2}y}{d{x}^2}=M(x)$

$EI$~~$EI\frac{dy}{dx}={\displaystyle \underset{0}{\overset{x}{}}}M(x)dx+C_1$

EIy$={\displaystyle \underset{0}{\overset{x}{}}}dn{t}_0^{x}M(x)dx+C_{1}x+C_2$ integrations $C1$ and $C2y(x)(x)$