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Scilab Help >> Differential calculus, Integration > integrate

# integrate

integration of an expression by quadrature

### Syntax

`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)```