Chapter 10.2, Problem 56E

To determine

(a)

To graph:

The Cornu’s spiral curve defined by parametric equations,

$x=C\left(t\right)={\int }_0^t\cos \left(\frac{\pi u^2}{2}\right)du$

$y=S\left(t\right)={\int }_0^t\sin \left(\frac{\pi u^2}{2}\right)du$

And then observe what happens as $t\to \infty \& as t\to -\infty$

To determine

(b)

To find:

The length of Cornu’s spiral from origin to the point with parameter value $t.$