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Scilab Help >> Differential Equations > integrate

integrate

integration of an expression by quadrature

Syntax

y = integrate(expr, v, x0, x1)
y = integrate(expr, v, x0, x1, atol)
y = 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-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 y(i) = integral_{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 - 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

History

VersionDescription
6.1.0 Default atol value increased from 10-14 to 10-13.

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