This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Documentation / Mathematica / Built-in Functions / Numerical Computation / Integration /


FilledSmallSquare Integrate[f, x] gives the indefinite integral .

FilledSmallSquare Integrate[f, x, xmin, xmax] gives the definite integral .

FilledSmallSquare Integrate[f, x, xmin, xmax, y, ymin, ymax] gives the multiple integral .

FilledSmallSquare Integrate[f, x] can be entered as f x.

FilledSmallSquare can be entered as AliasIndicatorintAliasIndicator or \[Integral].

FilledSmallSquare is not an ordinary d; it is entered as AliasIndicatorddAliasIndicator or \[DifferentialD].

FilledSmallSquare Integrate[f, x, xmin, xmax] can be entered with xmin as a subscript and xmax as a superscript to .

FilledSmallSquare Multiple integrals use a variant of the standard iterator notation. The first variable given corresponds to the outermost integral, and is done last.

FilledSmallSquare Integrate can evaluate integrals of rational functions. It can also evaluate integrals that involve exponential, logarithmic, trigonometric and inverse trigonometric functions, so long as the result comes out in terms of the same set of functions.

FilledSmallSquare Integrate can give results in terms of many special functions.

FilledSmallSquare Integrate carries out some simplifications on integrals it cannot explicitly do.

FilledSmallSquare You can get a numerical result by applying N to a definite integral.

FilledSmallSquare You can assign values to patterns involving Integrate to give results for new classes of integrals.

FilledSmallSquare The integration variable can be any expression. However, Integrate uses only its literal form. The object , for example, is not converted to .

FilledSmallSquare For indefinite integrals, Integrate tries to find results that are correct for almost all values of parameters.

FilledSmallSquare For definite integrals, the following options can be given:

FilledSmallSquare Integrate can evaluate essentially all indefinite integrals and most definite integrals listed in standard books of tables.

FilledSmallSquare In StandardForm, Integrate[f, x] is output as f x.

FilledSmallSquare See Section 1.4.4, Section 1.5.3 and Section 3.5.6.

FilledSmallSquare Implementation Notes: see Section A.9.5.

FilledSmallSquare See also: NIntegrate, DSolve, Sum, LaplaceTransform, FourierTransform.

FilledSmallSquare New in Version 1; modified in 5.0.

Further Examples