For the cantilever steel beam $[[$:$E=200$GPa;$I=129{10}^{6}m{m}^4\}$ shown in the figure, use the double$-$integration method to determine the deflection at A$.$ Assume $L=3\mathrm{.}8m,P=57kN,$ and $w_0=101k\frac{N}{m}.$

Part $1$

Write an equation for the internal moment in the beam as a function of location $x.$ Verify your equation by calculating the moment in the beam at two locations: $($a$)x=1\mathrm{.}27m,$ and $($b$)x=1\mathrm{.}9m.$ Enter your answers with the correct signs for the internal bending moment in the beam based on the sign convention.

$($a$)M=kN*m$

$($b$)M=kN*m$