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Scilab help >> Differential Equations, Integration > integrate

# integrate

integration of an expression by quadrature

### Calling Sequence

`x=integrate(expr,v,x0,x1 [,atol [,rtol]])`

### Arguments

expr

Character string defining a Scilab expression.

v

Character string, the integration variable name)

x0

real number, the lower bound of integration

x1

vector of real numbers, upper bounds of integration

atol

real number (absolute error bound) Default value: 1.-8

rtol

real number, (relative error bound) Default value: 1e-14

x

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

### Description

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

### Comments

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