Hp 50g Graphing Calculator Manual do Utilizador descarregar pdf (Página 449)

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101

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

) /dx = 3x

, an anti-derivative of f(x) = 3x

is F(x) = x

+ 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 +=

∫

)()(

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