using the beam theory.
1) draw a free body diagram and show the relation between distributed load q and the shear force V(x).
2) draw a free body digram and show the relation between V(x) and M(x).
So,
Relation between shear force and bending moment is,
M(x) = Differentiation (V(x))
Constant -> zero
Linear -> Constant
Parabolic -> Linear
Cubic Parabola -> Parabolic
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