SOLVE USING THE INTEGRATION METHOD

$7\mathrm{.}91$ The beam AB is subjected to the uniformly distributed load shown and to two unknown forces P and Q$.$ Knowing that it has been experimentally determined that the bending moment is $+20$kN$*$m at D and $+19$kN$*$m at E$,($a$)$ determine P and Q$,($b$)$ draw the shear and bending moment diagrams for the beam.

Answers: $($a$)$ P $=5$kN downwards, Q $=2$kN downwards

$($b$)$ V$\_$max $=16\mathrm{.}5$ kN at A; M$\_$max $=21\mathrm{.}5$ kNm$,2\mathrm{.}88$ m from A

SOLVE USING THE INTEGRATION METHOD