Rectangle Rule

Approximates the definite integral by using the rectangle rule.

Usage

integrate_rectangle(x, y, ...)

# S4 method for class 'numeric,numeric'
integrate_rectangle(x, y, right = FALSE)

# S4 method for class 'ANY,missing'
integrate_rectangle(x, right = FALSE)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

right

A logical scalar: should the right rule be used instead of the left rule?

Value

Returns a list with two components x and y.

See also

Other integration methods: integrate_trapezoid()

Author

N. Frerebeau

Examples

## Calculate the area under the sine curve from 0 to pi
# integrate(f = function(x) x^3, lower = 0, upper = 2)
x <- seq(0, 2, len = 101)
y <- x^3

plot(x, y, type = "l")


integrate_rectangle(x, y, right = FALSE) # 3.9204
#> [1] 3.9204
integrate_rectangle(x, y, right = TRUE) # 4.0804
#> [1] 4.0804
integrate_trapezoid(x, y) # 4.0004
#> [1] 4.0004