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Page 13-14
Anti-derivatives and integrals
An anti-derivative of a function f(x) is a function F(x) such that f(x) = dF/dx. For
example, since d(x
3
) /dx = 3x
2
, an anti-derivative of f(x) = 3x
2
is F(x) = x
3
+ C,
where C is a constant. One way to represent an anti-derivative is as a
indefinite integral
, i.e., , if and only if, f(x) = dF/dx, and
C = constant.
Functions INT, INTVX, RISCH, SIGMA and SIGMAVX
The calculator provides functions INT, INTVX, RISCH, SIGMA and SIGMAVX to
calculate anti-derivatives of functions. Functions INT, RISCH, and SIGMA work
with functions of any variable, while functions INTVX, and SIGMAVX utilize
functions of the CAS variable VX (typically, ‘x’). Functions INT and RISCH
require, therefore, not only the expression for the function being integrated, but
also the independent variable name. Function INT, requires also a value of x
where the anti-derivative will be evaluated. Functions INTVX and SIGMAVX
require only the expression of the function to integrate in terms of VX. Some
examples are shown next in ALG mode:
Please notice that functions SIGMAVX and SIGMA are designed for integrands
that involve some sort of integer function like the factorial (!) function shown
CxFdxxf +=
∫
)()(