Question $4$: A cantilevered beam $($fixed at the base$)$ is loaded with a uniformly distributed load acting over part of the span and a concentrated load acting $4$ m from the fixed end. The beam is rectangular in eross$-$section with a $209$ mm width and $600-mm$ deph. The beam is made from sieel having an allowable normal stress of $240$ MPa and elastic modulus of $200.$GPa.

$[18$ marks$]($a$)$ deternine the deflection and slope wit the free end of the beam using the method of integration.

$[2$ marks$]($b$)$ recognizing that computation of deflection can be a lengthy process using the method of integration, explain how you would compute the deflection of this beam in a design situation.

$($ please do the question neatly on a paper $)$