二重和三重积分

integral2 {pracma}

R Documentation

Numerically Evaluate Double and Triple Integrals

Description

Numerically evaluate a double integral, resp. a triple integral by reducing it to a double integral.

Usage

integral2(fun, xmin, xmax, ymin, ymax, sector = FALSE,
            reltol = 1e-6, abstol = 0, maxlist = 5000,
            singular = FALSE, vectorized = TRUE, ...)

integral3(fun, xmin, xmax, ymin, ymax, zmin, zmax,
            reltol = 1e-6, ...)

Arguments

fun	function
xmin, xmax	lower and upper limits of x.
ymin, ymax	lower and upper limits of y.
zmin, zmax	lower and upper limits of z.
sector	logical.
reltol	relative tolerance.
abstol	absolute tolerance.
maxlist	maximum length of the list of rectangles.
singular	logical; are there singularities at vertices.
vectorized	logical; is the function fully vectorized.
..	additional parameters to be passed to the function.

example

 

 

 double<-function(x,y){ + ifelse(x+y>=1,6*x*y^2,0)} 

> integral2(double,0,1,0,1) $Q
[1] 0.9072746

$error
[1] 7.325264e-08

 

 
  

> double<-function(x,y){ + 6*x*y^2} > 

integral2(double,1/2,3/4,0,1) 

$Q
[1] 0.3125

$error
[1] 6.938894e-18