Question

Carry out the integrals

x(t)= $\intop$₀^t (cos($\pi$u²/2)du) ; y(t)= $\intop$₀^t (sin($\pi$u²/2)du

for a large number of values of t in the interval [0, N], where N is a large number (20, say, which you can change) and plot the values on a x-y plane. Get the beautiful Cornu spiral, which you can get on the internet. Use both Simpson rule and Gaussian quadrature.