Double and Triple Integration

Numerically evaluate double integral over rectangle.

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

triplequad(f, xa, xb, ya, yb, za, zb, 
            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.

za, zb

left and right endpoint for third 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.

Details

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

Function triplequad reduces the problem to dblquad by first integrating over the innermost variable.

Value

Numerical scalar, the value of the integral.

See also

integrate, quad2d, simpson2d

Examples

f1 <- function(x, y) x^2 + y^2
dblquad(f1, -1, 1, -1, 1)       #   2.666666667 , i.e. 8/3 . err = 0
#> [1] 2.666667

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
#> [1] -9.869604

# 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
#> [1] 2.094395

f4 <- function(x, y, z) y*sin(x)+z*cos(x)
triplequad(f4, 0,pi, 0,1, -1,1) # - 2.0 => -2.220446e-16
#> [1] 2