Sigma , Riemann Sums
                              Definite Integrals

                                Mathematica

Dr. Andrzej Korzeniowski
Department of Mathematics, UTA

Lesson 5  

Mathematica built-in symbolic summation is a great tool for finding Riemann sums of elementary functions.
Below are several examples.

Consider  the function  and suppose we need to find the area below its graph and above x - axis
over the interval  [1, 2] .   

which leads to the same by

or

To find the numerical value directly

or use the numerical procedure (especially  in the case when indefinite integral cannot be found)