# 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 : x (i) = ∫ x 0 x 1 (i) f (v) dv x(i)=int_{x_0}^{x_1(i)} f(v)dv for `i=1:size(x1,'*')` where f(v) 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
- inttrap
- intsplin
- ode