Mathematica 9 is now available

Documentation / CalculationCenter / Functions / Calculus /

Integrate

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 can be used to find the area under a curve or the accumulated total of a continuous function.

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

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

FilledSmallSquare Integrate[f, x] is output as .

FilledSmallSquare See also: NIntegrate, NSum, SolveODE.

Examples

Using InstantCalculators

Here are the InstantCalculators for the Integrate function. Enter the parameters for your calculation and click Calculate to see the result.

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Entering Commands Directly

Indefinite integral

You can paste a template for this command via the Text Input button on the Integrate Function Controller.

Indefinite integrals

Here are two indefinite integrals.

In[3]:=

Out[3]=

In[4]:=

Out[4]=

Here is an indefinite integral that is evaluated by special table lookup rules.

In[5]:=

Out[5]=

Definite integrals

Here are two definite integrals.

In[6]:=

Out[6]=

In[7]:=

Out[7]=

Ordinary Mathematical Notation

Indefinite integral

This also gives the indefinite integral of .

In[8]:=

Out[8]=

Definite integral

This also gives the definite integral of from -1 to 1.

In[9]:=

Out[9]=



Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.