# integrate.box {voronoi}

Integral over a rectangular region

### Description

Calculates the integral of a function over a rectangular region in the plane.

### Usage

integrate.box(x.lims, y.lims, f = NULL, antideriv.x = NULL, antideriv.y = NULL)

### Arguments

- x.lims
- A vector of length 2 describing the lower and upper limits of integration in the x-direction.
- y.lims
- A vector of length 2 describing the lower and upper limits of integration in the y-direction.
- f
- A function taking two arguments that is to be integrated over the specified region.
- antideriv.x
- A function taking two arguments that is the antiderivative of
`f`

with respect to x. - antideriv.y
- A function taking two arguments that is the antiderivative of
`f`

with respect to y.

### Details

Only one of `f`

, `antideriv.x`

, or `antideriv.y`

need be specified. Specification of either of the antiderivatives yields more efficient performance by reducing the dimension in which integration is performed.

### Values

The scalar result of the integration.

### See Also

`centroidal`

, `polygon.adapt`

### Examples

func <- function(x, y) x + y^3 integrate.box(x.lims = c(0,4), y.lims = c(2,4), f = func) antideriv.x <- function(x, y) x^2/2 + x*y^3 integrate.box(x.lims = c(0,4), y.lims = c(2,4), antideriv.x = antideriv.x) antideriv.y <- function(x, y) x*y + y^4/4 integrate.box(x.lims = c(0,4), y.lims = c(2,4), antideriv.y = antideriv.y)

Documentation reproduced from package voronoi, version 1.1. License: GPL-3