We must derive an equation for the bending moment M(x) that acts internally at every point in the interval between x = 0 and x = L.
Once M(x) has been derived, the moment equation will be integrated to find the beam slope. A second integration will be performed to find the elastic curve equation v(x).
In integrating M(x), two constants of integration will emerge. To evaluate these constants, appropriate boundary conditions for the beam will be noted and used to determine the constants of integration.