Question 182
Compute the limit
$$
\lim_{n \to \infty} \frac{1}{n} \sum_{k=0}^{n-1} k \int_{\frac{k}{n}}^{\frac{k+1}{n}} \sin(\pi x^2) dx.
$$
$$
\lim_{n \to \infty} \frac{1}{n} \sum_{k=0}^{n-1} k \int_{\frac{k}{n}}^{\frac{k+1}{n}} \sin(\pi x^2) dx.
$$