Integral
Calculator using Scilab
We
can use Scilab as a definite integral calculator. The numerical integration of
functions in one
dimension can be
performed with intg(a,
b, f) and it’s very easy to use. First,
we define the function to
integrate...
In this example, we define
it in a single line, but it can
also
be defined by writing
a separate file
and uploading it.
Second, we call
intg with the limits of the integral.
If the function
has other arguments besides
the variable
of integration, you can
use a list. This
definite integral:
Can be calculated
in Scilab, like this, in two lines:
function
y = f(x), y = exp(x^2), endfunction
I =
intg(1/2, 3/2,
f)
and the answer is
I =
0.3949074
Notice that we
can define the function to be integrated in just one line, if the
function is
simple. We can also use the function deff for the definition of the
function,
like this:
deff('y
= f(x)',
'y = exp(x^2)')
Integration
with Matlab
If we happen to
need the integration of this other function, where we have to calculate
the
absolute value of the sine function, from –pi to pi radians
we can calculate
it like this
function y =
f1(x), y = abs(sin(x)), endfunction
I =
intg(%pi,
%pi, f1)
and the answer is
I = 4
There are specialized functions to integrate 2D
and 3D.
As usual, the best reference for the syntax and examples is the online
help. Just
type "help" (or "help function"
without quotes) on your command window.
Function int2d
uses an adaptive algorithm in which if a function is rapidly changing,
it is
divided into finer grids and the integral is recalculated until a
convergence
is achieved. These type of algorithms are included in many of Scilab’s
(or
Scicoslab’s) builtin functions such as intg or integrate.
For
example,
the function int2d performs
definite twodimensional integrals by the quadrature
and cubature methods. The calling sequence is
[I,
err] = int2d(X,
Y, f [,params])
The
region of integration is determined by
a series
of triangles whose vertices
are
passed through two
matrices (X and Y). These vectors have
dimension 3xN,
where N is the
number of triangles
and indicates
each coordinate
of the vertices
of the triangles.
The
following example computes
the integrand over the two triangles with coordinates (0, 0), (5, 5),
(5, 0)
and (0, 0), (0, 5) and (5, 5). This describes the rectangle from (0, 0)
to (5, 5)
and parallel lines to the axes.
X = [0 0; 5 5; 5 0];
Y = [0
0; 0 5; 5 5];
function
z = f(x, y), z = cos(x + y), endfunction
[I,
error] = int2d(X, Y, f)
the result is
error = 1.078D09
I =
0.4063959
From
'Integral Calculator' to Matlab home
From
'Integral Calculator' to Scilab menu
