Simpson's 3/8 rule

Source: R/simp38.R

Use Simpson's 3/8 rule to integrate a function

simp38(f, a, b, m = 100)

Arguments

f

function to integrate
a

the a-bound of integration
b

the b-bound of integration
m

the number of subintervals to calculate

Value

the value of the integral

Details

The simp38 function uses Simpson's 3/8 rule to calculate the integral of the function f over the interval from a to b. The parameter m sets the number of intervals to use when evaluating. Additional options are passed to the function f when evaluating.

See also

Other integration: adaptint(), gaussint(), giniquintile(), mcint(), midpt(), revolution-solid, romberg(), simp(), trap()

Other newton-cotes: adaptint(), giniquintile(), midpt(), romberg(), simp(), trap()

Examples

f <- function(x) { sin(x)^2 + log(x) }
simp38(f, 1, 10, m = 10)
#> [1] 18.52477
simp38(f, 1, 10, m = 100)
#> [1] 18.52494
simp38(f, 1, 10, m = 1000)
#> [1] 18.52494