p.386, Ex.7 (Chapter 7)

Exercise

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

  1. \(f(x) = 2x^{\frac{3}{2}}-\frac{1}{6}\sqrt{(x)}\) on \([0,9]\)

Solution

library(pracma)

f <- function(x) 2 * x^(3/2) - 1/6* sqrt(x)
F <- function(x) c(x, f(x))
arclength(F, a=0, b=9)
## $length
## [1] 54.49999
## 
## $niter
## [1] 15
## 
## $rel.err
## [1] 9.685107e-06

The arc length of the function is 54.5