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