Please notice that functions SIGMAVX and SIGMA are designed for integrands that involve some sort of integer function like the factorial (!) function shown above. Their result is the so-called discrete derivative, i.e., one defined for integer numbers only.

Definite integrals

In a definite integral of a function, the resulting anti-derivative is evaluated at the upper and lower limit of an interval (a,b) and the evaluated values subtracted. Symbolically, we write

b

∫

a

f (x)dx = F (b) − F (a),

where f(x) = dF/dx.

To calculate definite integrals of functions using the CAS variable VX (typically, ‘X’), use function PREVAL(f(x),a,b). For example,

Infinite series

A function f(x) can be expanded into an infinite series around a point x=x0 by using a Taylor’s series, namely,

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