# 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 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

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