Numeric integration of symbolic expressions is performed in newRPL via the NUMINT command which implements the Adaptive Simpson's method.

NUMINT accepts four arguments:

• the mono-variate function to integrate, either in symbolic or program form;
• the lower integration limit;
• the upper integration limit;
• the error tolerance.

If the function to integrate is expressed in symbolic form it must respect a precise syntax:

• it must be written as an equation;
• the left side must be in the form func(var) where var is the integrating variable and func is the function's name;
• the right side is a function, expressed in terms of var.

For example valid expressions are:

'F(X)=X*LN(X)'
'G(Z)=Z^2-2*COS(Z)'
'VEL(T)=ACC*T'

As shown above, the functions may refer to global or local variables; the function's name is only descriptive and bears no relevance to the calculation.

Alternatively, the function can be written as a program which accepts exactly one numeric argument and returns exactly one numeric result. The expressions above can be rewritten as:

« DUP LN * »
« DUP SQ SWAP COS 2 * - »
« 'ACC' RCL * »

The integration limits can be either real or complex finite numbers; symbolic constants are accepted and silently converted to numerical values.

The error tolerance is a real number used to specify the required precision of the calculation: when two successive iterations differ by a value which is less than the tolerance the calculation stops.