The Riemann Sum

 

In a Nut Shell:  Selection of the location of the sampling points effects the estimation

of the area.  It differs for increasing and for decreasing functions.   Selection of mid-

points provides a better approximation of the area.

 

         

The figures below depict the effect of sampling points on estimation of areas for

increasing and for decreasing functions.

 

 

 

                               

 

 

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