I am trying to derive the maximum deflection of a cantilever beam. L is the length of the beam and a is the where force is applied.
For the case 0<x<a, I use the method below and it gives me the same result of well known formulas. $$M \left( x \right) ={\it Heaviside} \left( a-x \right) F \left( a-x \right)$$
$$\delta=\int_{0}^{a}\!{\frac {M \left( x \right) \partial \left( M \left( x \right) \right) }{EI\partial \left( F \right) }}\,{\rm d}x $$
For case a<x<L, which method should I follow?