For a cantilever beam subjected to a triangular distributed load, what is the order of the internal moment expression of the beam as a function of the location

The Order is 4th order

Explanation:

Let take the diagram on the first uploaded image as an example of triangular distributed load  

Let x denote the location

To obtain the vertical force acting at point a we integrate the function  

    where is the vertical force

    dx is the change in location

     w is a single component of force acting downwards

                 =  

To obtain the moment of of inertia \

To obtain the shear force acting at a distance x from A

   To obtain the moment about the triangular distributed load section that is at a distance x from A as shown on the diagram

       = >    

          =>        

      =>          

Looking at this equation as a polynomial we see that the order is 4 i.e