integrate

Scilab Function
Last update : 23/06/2004

integrate - integration by quadrature

### Calling Sequence

  `[x]=integrate(expr,v,x0,x1 [,ea [,er]])`

### Parameters

- `expr`: external Scilab
- `v`: string (integration variable)
- `x0,x1`: real numbers (bounds of integration)
- `ea,er`: real numbers (absolute error bound) Default value: 0
- `er`: real number, (relative error bound) Default value: 1.d-8

### Description

computes :

                           /x1
                          [
                      x = I  f(v)dv
                          ]
                         /x0

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

### Examples

    integrate('sin(x)','x',0,%pi)
    integrate(['if x==0 then 1,';
               'else sin(x)/x,end'],'x',0,%pi)

### See Also

`intg`, `inttrap`, `intsplin`, `ode`,