pracma (version 1.1.6)

dblquad: Double Integration

Description

Numerically evaluate double integral over rectangle.

Usage

dblquad(f, xa, xb, ya, yb, dim = 2, ..., 
        subdivs = 300, tol = .Machine$double.eps^0.5)

Arguments

f

function of two variables, the integrand.

xa, xb

left and right endpoint for first variable.

ya, yb

left and right endpoint for second variable.

dim

which variable to integrate first.

subdivs

number of subdivisions to use.

tol

relative tolerance to use in integrate.

...

additional parameters to be passed to the integrand.

Value

• Numerical scalar, the value of the integral.

Details

This function applies the internal single variable integration function integrate two times, once for each variable.

See Also

integrate, quad2d

Examples

f1 <- function(x, y) x^2 + y^2
dblquad(f1, -1, 1, -1, 1)     #   2.666666667 , i.e. 8/3 . err = 0

f2 <- function(x, y) y*sin(x)+x*cos(y)
dblquad(f2, pi, 2*pi, 0, pi)  #  -9.869604401 , i.e. -pi^2, err = 0

# f3 <- function(x, y) sqrt((1 - (x^2 + y^2)) * (x^2 + y^2 <= 1))
f3 <- function(x, y) sqrt(pmax(0, 1 - (x^2 + y^2)))
dblquad(f3, -1, 1, -1, 1)     #   2.094395124 , i.e. 2/3*pi , err = 2e-8