Manual HP 49g graphing calculator (page 137 of 175) (English)

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Anti-derivatives and integrals

An anti-derivative of a function f(x) is a function F(x) such that f(x) = dF/dx.

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. Functions INTVX, RISCH, SIGMA and SIGMAVX are available in the

CALC/DERIV&INTEG menu, while INT is available in the command catalog.

Some examples are shown next in ALG mode (type the function names to

activate them):

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HP 49g graphing calculator Manual

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