Discussion 13

Using R, provide the solution for any exercise in either Chapter 4 or Chapter 7 of the calculus textbook. If you are unsure of your solution, post your concerns. Chapter 7.4 Problem 5 In Exercises3-13,???nd the arc length of the function on the given interval.

f(x)=1/3x3/2???x1/2 on [0,1] Define Function

library(pracma)
f<-function(x) 1/3 * x^(3/2)- x^(1/2)
x <- seq(0,1,0.01)
plot(x,f(x), type="l",
     xlab="x", ylab="f(x)", main="f(x) on [0,1]")

#Converting the function to parameterized function
F <- function(x) c(x, f(x))

# Find arc length
arclength(F, a=0, b=1)
## $length
## [1] 1.333331
## 
## $niter
## [1] 11
## 
## $rel.err
## [1] 3.825585e-06