Use the Cornu spiral

On the Cornu spiral in an optics textbook take a sequence of values of $w$ from $-4.0$ to $+4.0$ in steps of $0.1$ and measure the line length $L$ from the lower asymptote to the curve. Notice that this must be measured on the same scale as the one on which the spiral is plotted. Plot a graph of $L^2/2$ versus $w$. The first maximum will occur around $w = 1.2$. Estimate from this graph the values of $w$ corresponding to the maxima and minima you found. Calculate the $x$ values expected for these maxima and minima by evaluating equation 9.2in each case, and compare with the measurements. Explain any systematic error you find in this comparison.