Chapter 7 Section 4 Exercise 6, page 386,

textbook: Apex Calculus 1

Find the arc length of the function on the given interval.

\[7. \quad f(x) = \frac{1}{12}x^{3}-\frac{1}{x} \quad on \quad [1, 4]\]

y = function(x) {
  return((1/12*(x^3)) - (x^-1))
}
## draw the arc to investigate the shape
## 
x = seq(0, 5, 0.1)
plot(x, y(x), type = 'l', col ='red')

library(pracma)
# Parameterize x as a function of y
f_x <- function(x){
  c(x, y(x))
}
print(arclength(f_x, 1, 4)$length)
## [1] 6.821297