Sigma [Graphics:Images/lesson5_gr_1.gif] , 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.

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Consider  the function  [Graphics:Images/lesson5_gr_10.gif]and suppose we need to find the area below its graph and above x - axis
over the interval  [1, 2] .   

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which leads to the same by

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or

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To find the numerical value directly

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or use the numerical procedure (especially  in the case when indefinite integral [Graphics:Images/lesson5_gr_40.gif] cannot be found)

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Converted by Mathematica      March 27, 2001