Chapter 6.4, Problem 213E

Draw graphs of $y=x^2,y=x^6$ and $y=x^{10}$ . For $y=x^n$, as n increases, formulate a prediction on the arc length from $\left(0,0\right)$ to $\left(1,1\right)$ . Now, compute the lengths of these three functions and determine whether your prediction is correct.