Simpson's rule

Use Simpson's rule to integrate a function

simp(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 simp function uses Simpson's 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(), simp38(), trap()

Other newton-cotes: adaptint(), giniquintile(), midpt(), romberg(), simp38(), trap()

Examples

f <- function(x) { sin(x)^2 + cos(x)^2 }
simp(f, -pi, pi, m = 10)
#> [1] 6.283185
simp(f, -pi, pi, m = 100)
#> [1] 6.283185
simp(f, -pi, pi, m = 1000)
#> [1] 6.283185