Integrate
Integrate[
f
,
x
]
gives the indefinite integral
.
Integrate[
f
,
{
x
,
xmin
,
xmax
}
]
gives the definite integral
.
Integrate[
f
,
{
x
,
xmin
,
xmax
}
,
{
y
,
ymin
,
ymax
}
]
gives the multiple integral
.
Integrate
can be used to find the area under a curve or the accumulated total of a continuous function.
Integrate[
f
,
x
]
can be entered as
.
can be entered as
int
or
\
[Integral]
.
is not an ordinary
d
; it is entered as
dd
or
\
[DifferentialD]
.
Integrate[
f
,
{
x
,
xmin
,
xmax
}
]
can be entered with
xmin
as a subscript and
xmax
as a superscript to
.
Multiple integrals use a variant of the standard iterator notation. The first variable given corresponds to the outermost
integral, and is done last.
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.
Integrate
can give results in terms of many special functions.
Integrate
carries out some simplifications on integrals it cannot explicitly do.
The integration variable can be any expression. However,
Integrate
uses only its literal form. The object
, for example, is not converted to
.
For indefinite integrals,
Integrate
tries to find results that are correct for almost all values of parameters.
Integrate
can evaluate essentially all indefinite integrals and most definite integrals listed in standard books of tables.
Integrate[
f
,
x
]
is output as
.
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]:=
In[4]:=
Here is an indefinite integral that is evaluated by special table lookup rules.
In[5]:=
Definite integrals
Here are two definite integrals.
In[6]:=
In[6]:=
Out[6]=
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]=
