HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 449)

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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

) /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., CxFdxxf +=

∫

)()( , 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:

1 2 ... 444 445 446 447 448 449 450 451 452 453 454 ... 863 864

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