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(append) ¥ p
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string1
‰ ‰ ‰ ‰ ()
(integrate) 2 <
‰ ‰ ‰ ‰ ( expression1 var
,
‰ ‰ ‰ ‰ ( list1,var order
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‰ ‰ ‰ ‰ ( matrix1,var order
[,
Returns the integral of
the variable
Returns an anti-derivative if
omitted. A symbolic constant of integration such
as is omitted.
C
However,
integration if only
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
()
cannot determine as an explicit finite
combination of its built-in functions and
operators.
When
lower
attempt is made to locate any discontinuities or
discontinuous derivatives in the interval
var < upper
places.
For the
numerical integration is used where applicable
when an anti-derivative or a limit cannot be
determined.
For the
tried first, if applicable. Anti-derivatives are
sought only where such numerical integration is
inapplicable or fails.
‰
can be nested to do multiple integrals.
()
Integration limits can depend on integration
variables outside them.
Note: See also
Appendix A: Functions and Instructions
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matrix
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var from lower to upper
lower
is added as a constant of
lower
is omitted.
upper
expression1
and are both present, an
upper
and to subdivide the interval at those
setting of the
AUTO Exact/Approx
setting, numerical integration is
APPROX
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