For exact (symbolic) integrations and solutions, see ** Symbolic Math**.

There are three functions available for numerical integration.
The functions **quad** and **quad8** use adaptive, recursive
rules, the low order Simpson's and the higher order Newton Cotes 8 panel
respectively; other than the rule used, they act identically.
The basic format is **quad(' function', start, finish)**
to get the integral of

If the integration requires too much recursion (e.g. if the integral
is singular), the value **Inf** is returned.

An optional fourth argument may be specified to give the tolerance (default . An optional boolean fifth argument may then be given to specify whether the evalutions should be traced in a point plot automatically (False if 0, True otherwise). An empty matrix may be passed for either of these to keep the defaults.

If *function* takes more than one argument, the others may be
specified as constant (for the integration) parameters by
**quad(' function', start, finish, tolerance,
trace, first parameter, second parameter...)**. This
integrates

Alternatively, **trapz** may be used for trapezoidal numerical
integration; the format is **trapz(x, y)**. Here *x* is a vector
and *y* is a matrix of any number of columns, but as many rows as
the length of *x*. Each column of *y* is considered to be a function
over *x* and is integrated with the trapezoidal approximation. The
result is a vector of the column integrations. If *x* is omitted,
unit spacing between points is assumed.

Sat Mar 21 21:42:28 EST 1998