Calculate the deflection and rotation at the mid$-$span of the beam shown in Figure $1$ using the

double integration method

$(1\mathrm{.}45$ marks$)$

Calculate the deflection and rotation at the free end of the cantilever beam shown in Fig $2$

using the conjugate beam analogy method leaving your answers in EI$.$

$(1\mathrm{.}45$ marks$)$