Question

find the arc length of the funcƟon on the given interval

\[f(x)=\dfrac{1}{12}x^5 + \dfrac{1}{5x^3}\] on [0.1,1]

library(pracma)
## Warning: package 'pracma' was built under R version 3.6.3
gn_funct <- function(x) ({1/12}*x^5+(1/5*x^3))
gn_funct
## function(x) ({1/12}*x^5+(1/5*x^3))
x <- seq(0,1,0.1)
x
##  [1] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
plot(x, gn_funct(x), type='l', col="green", xlab="x-Axis", ylab="y-Axis")

len_funct <- function(x) {c(x,gn_funct(x))}
len_funct
## function(x) {c(x,gn_funct(x))}
arc_l <- arclength(len_funct,0.1,1)
arc_l
## $length
## [1] 0.9728843
## 
## $niter
## [1] 5
## 
## $rel.err
## [1] 1.84336e-06
arc_l$length  
## [1] 0.9728843

The ARC Length is 0.973