---
name: "integrate"
section: "4rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.0-2+b1"
release: "Debian 10 (Buster)"
platforms: ["linux"]
url: "https://new.carta.tech/integrate/4rheolef"
---

# integrate(4rheolef)

integrate a function or an expression

## NAME

**integrate** - integrate a function or an expression

## DESCRIPTION

Integrate an expression over a domain by using a quadrature formulae. There are three main usages of the integrate function, depending upon the type of the expression. (i) When the expression is a numerical one, it leads to a numerical value. (ii) When the expression involves a symbolic test-function see test(2), the result is a linear form, represented by the **field** class. (iii) When the expression involves both  symbolic trial- and test-functions see test(2), the result is a bilinear form, represented by the **field** class.

## SYNOPSIS

```
 Float integrate (geo domain);
 Float integrate (geo domain, quadrature_option qopt);
 Value integrate (geo domain, Expression, quadrature_option qopt);
```

 field integrate (Expression);\
  field integrate (Expression, quadrature\_option qopt);\
  field integrate (geo domain, Expression);\
  field integrate (geo domain, Expression, quadrature\_option qopt);

 form integrate (Expression);\
  form integrate (Expression, integrate\_option qopt);\
  form integrate (geo domain, Expression);\
  form integrate (geo domain, Expression, integrate\_option qopt);

## EXAMPLE

For computing the measure of a domain:

```
  Float meas_omega = integrate (omega);

```

For computing the integral of a function:

```
  Float f (const point& x);
  ...
  quadrature_option qopt;
  qopt.set_order (3);
  Float int_f = integrate (omega, f, qopt);

```

The last argument specifies the quadrature formulae (see quadrature\_option(2)) used for the computation of the integral. The function can be replaced by any field-valued expression (see field(2)). For computing a right-hand-side of a variational formulation with the previous function **f**:

```
  space Xh (omega, "P1");
  test v (Xh);
  field lh = integrate (f*v);

```

For computing a bilinear form:

```
  trial u (Xh);
  test v (Xh);
  form m = integrate (u*v);

```

The expression **u\*v** can be replaced by any bilinear expression (see field(2)).

## DEFAULT ARGUMENTS

In the case of a linear or bilinear form, the domain is optional: by default it is the full domain definition of the test function. Also, the quadrature formulae is optional: by default, its order is **2\*k+1** where **k** is the polynomial degree of the **Xh** space associated to the test function **v**. When both a test **u** and trial **v** functions are supplied, let k1 and k2 be their polynomial degrees. Then the default quadrature is chosen to be exact at least for k1+k2+1 polynoms. When the integration is performed on a subdomain, this subdomain simply replace the first argument and a domain name could also be used:

```
  field l2h = integrate (omega["boundary"], f*v);
  field l3h = integrate ("boundary", f*v);

```

For convenience, only the domain name can be supplied.

## SEE ALSO

test(2), test(2), quadrature\_option(2), field(2), field(2)

## COPYRIGHT

Copyright (C) 2000-2018 Pierre Saramito \<Pierre.Saramito@imag.fr\> GPLv3+: GNU GPL version 3 or later \<http://gnu.org/licenses/gpl.html\>. This is free software: you are free to change and redistribute it.  There is NO WARRANTY, to the extent permitted by law.