Problem $3$

$[25$ points$]$

Consider the beam of length $L$ shown in the figure below loaded with a vertical load P $.$ The elastic modulus is E and the cross$-$sectional moment of inertia is I.

a$)$ Integrate the internal bending moment to find an expression for the deflection of the beam. Clearly state the differential equation and boundary conditions you are using.

$[20$ points$]$

b$)$ Without performing any calculations, describe in words how you would solve for the deflection if the beam section from