integrate

integration of an expression by quadrature

Calling Sequence

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

Arguments

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

Description

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)