Graphics Programs Reference
In-Depth Information
Integration
MATLAB can compute definite and indefinite integrals. Here is an indefinite
integral:
>> int ('xˆ2', 'x')
ans =
1/3*x^3
As with
diff
, you can declare
x
to be symbolic and dispense with the char-
acter string quotes. Note that MATLAB does not include a constant of inte-
gration; the output is a single antiderivative of the integrand. Now here is a
definite integral:
>> syms x; int(asin(x), 0, 1)
ans =
1/2*pi-1
You are undoubtedly aware that not every function that appears in calcu-
lus can be symbolically integrated, and so numerical integration is sometimes
necessary. MATLAB has three commands for numerical integration of a func-
tion
f
(
x
):
quad
,
quad8
, and
quadl
(the latter is new in MATLAB 6). We
recommend
quadl
, with
quad8
as a second choice. Here's an example:
>> syms x; int(exp(-xˆ4), 0, 1)
Warning: Explicit integral could not be found.
> In /data/matlabr12/toolbox/symbolic/@sym/int.m at line 58
ans =
int(exp(-x^4),x=0..1)
>> quadl(vectorize(exp(-xˆ4)), 0, 1)
ans =
0.8448
➱
The commands
quad
,
quad8
, and
quadl
will not accept
Inf
or
-Inf
as
a limit of integration (though
int
will). The best way to handle a
numerical improper integral over an infinite interval is to evaluate
it over a
very large
interval.
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