Scilab Function

intg - definite integral

### Calling Sequence

  `[v,err]=intg(a,b,f [,ea [,er])`

### Parameters

- `a,b` : real numbers
- `f` : external (function or list or string)
- `ea, er` : real numbers
- `ea` : absolute error required on the result. Default value: 0
- `er` : relative error required on the result. Default value: 1.d-8
- `err` : estimated absolute error on the result.

### Description

`intg(a,b,f)` evaluates the definite integral from `a` to `b` of `f(t)dt`. The evaluation hopefully satisfies following claim for accuracy: `abs(I-v)<= max(ea,er*abs(I))` where I stands for the exact value of the integral.

`f` is an external :

If `f` is function its definition must be as follows `y = f(t)`

If `f` is a list the list must be as follows: `list(f,x1,x2,...)` where `f` is a function with calling sequence `f(t,x1,x2,...)`.

If `f` is a string it refers to a the name of a Fortran subroutine (see source code of `fintg.f`)

### Examples

    deff('[y]=f(x)','y=x*sin(30*x)/sqrt(1-((x/(2*%pi))^2))')
    exact=-2.5432596188;
    abs(exact-intg(0,2*%pi,f))
    // See file routines/default/Ex-intg.f
    abs(exact-intg(0,2*%pi,'intgex'))

### See Also

`intc` `intl` `inttrap` `intsplin` `ode`