integrate

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-13.

rtol

a real number, (relative error bound). Default value: 1e-8.

y

a vector of real numbers, the integral value for each x1(i).

Description

y = integrate(expr, v, x0, x1 [,atol [,rtol]]) computes for i=1:size(x1,'*'), where f(v) is given by the expression expr.

The evaluation hopefully satisfies following claim for accuracy: abs(I - y) <= max(atol, rtol*abs(I)) where I stands for the exact value of the integral.

Restriction: The given expression must not use variable names with a leading %.

Examples

x1 = 0:0.1:2*%pi;
Y = integrate('sin(x)', 'x', 0, x1);
norm(cos(x1)-(1-Y))

x1 = -10:0.1:10;
Y = 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

History