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Sigma , Riemann Sums

Definite Integrals

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*Mathematica*

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Dr. Andrzej Korzeniowski*

Department of Mathematics, UTA

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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)

Converted by *Mathematica*
March 27, 2001