Application Guide

222 Symbols
∫() (integral)
Catalog >
Returns the integral of Expr1 with respect
to the variable Var from Lower to Upper.
Note: See also Definite or Indefinite integral
template, page 6.
Note: You can insert this function from the
keyboard by typing integral(...).
If Lower and Upper are omitted, returns an
anti-derivative. A symbolic constant of
integration is omitted unless you provide
the Constant argument.
Equally valid anti-derivatives might differ by
a numeric constant. Such a constant might
be disguised—particularly when an anti-
derivative contains logarithms or inverse
trigonometric functions. Moreover,
piecewise constant expressions are
sometimes added to make an anti-
derivative valid over a larger interval than
the usual formula.
∫() returns itself for pieces of Expr1 that it
cannot determine as an explicit finite
combination of its built-in functions and
operators.
When you provide Lower and Upper, an
attempt is made to locate any
discontinuities or discontinuous derivatives
in the interval Lower < Var < Upper and to
subdivide the interval at those places.
For the Auto setting of the Auto or
Approximate mode, numerical integration is
used where applicable when an anti-
derivative or a limit cannot be determined.
For the Approximate setting, numerical
integration is tried first, if applicable. Anti-
derivatives are sought only where such
numerical integration is inapplicable or
fails.
Note: To force an approximate result,
Handheld: Press / ·.
Windows®: Press Ctrl+Enter.
Macintosh®: Press “+Enter.
iPad®: Hold enter, andselect .