integrate
=========

integration of an expression by quadrature



Calling Sequence
~~~~~~~~~~~~~~~~


::

    x=integrate(expr,v,x0,x1 [,atol [,rtol]])




Arguments
~~~~~~~~~

:expr a character string defining a Scilab expression.
: :v a character string, the integration variable name.
: :x0 a real number, the lower bound of integration.
: :x1 a vector of real numbers, upper bounds of integration.
: :atol a real number (absolute error bound). Default value: 1e-8.
: :rtol a real number, (relative error bound). Default value: 1e-14.
: :x a vector of real numbers, the integral value for each `x1(i)`.
:



Description
~~~~~~~~~~~

`x=integrate(expr,v,x0,x1 [,atol [,rtol]])` computes : for
`i=1:size(x1,'*')` where is given by the expression `expr`.

The evaluation hopefully satisfies following claim for accuracy:
`abs(I-x)<= max(atol,rtol*abs(I))` where `I` stands for the exact
value of the integral.



Restriction
~~~~~~~~~~~

The given expression should not use variable names with a leading `%`.



Examples
~~~~~~~~


::

    x0=0;x1=0:0.1:2*%pi;
    X=integrate('sin(x)','x',x0,x1);
    `norm`_(`cos`_(x1)-(1-X))
    
     x1=-10:0.1:10;
    X=integrate(['if x==0 then 1,';
                 'else sin(x)/x,end'],'x',0,x1)




See Also
~~~~~~~~


+ `intg`_ definite integral
+ `inttrap`_ integration of experimental data by trapezoidal
  interpolation
+ `intsplin`_ integration of experimental data by spline interpolation
+ `ode`_ ordinary differential equation solver


.. _intsplin: intsplin.html
.. _inttrap: inttrap.html
.. _intg: intg.html
.. _ode: ode.html