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Functions DERIV and DERVX
The function DERIV is used to take derivatives in terms of any independent
variable, while the function DERVX takes derivatives with respect to the
CAS default variable VX (typically ‘X’). While function DERVX is available
directly in the CALC menu, both functions are available in the
DERIV.&INTEG sub-menu within the CALCL menu (
„Ö).
Function DERIV requires a function, say f(t), and an independent variable,
say, t, while function DERVX requires only a function of VX. Examples are
shown next in ALG mode. Recall that in RPN mode the arguments must be
entered before the function is applied.
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.,
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):
CxFdxxf +=
∫
)()(
SG49A.book Page 3 Friday, September 16, 2005 1:31 PM