Chapter 10, Problem 7PS

Cornu Spiral Consider the cornu spiral given by

$x(t)={\displaystyle {\int }_0^t\cos \frac{\pi u^2}{2}du}$ and $y(t)={\displaystyle {\int }_0^t\sin \frac{\pi u^2}{2}du}$.

(a) Use a graphing utility to graph the spiral over the interval $-\pi \le t\le \pi$.

(b) Show that the cornu spiral is symmetric with respect to the origin.

(c) Find the length of the comu spiral from $t=0$ to $t=a$. What is the length of the spiral from $t=-\pi$ to $t=\pi ?$