Câu hỏi 188
a. Tính
$$
\int_{0}^{1} x \sin \left(\pi x^{2}\right) \mathrm{d} x
$$
b. Tính
$$
\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{k=0}^{n-1} k \int_{\frac{k}{n}}^{\frac{k+1}{n}} \sin \left(\pi x^{2}\right) \mathrm{d} x
$$
$$
\int_{0}^{1} x \sin \left(\pi x^{2}\right) \mathrm{d} x
$$
b. Tính
$$
\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{k=0}^{n-1} k \int_{\frac{k}{n}}^{\frac{k+1}{n}} \sin \left(\pi x^{2}\right) \mathrm{d} x
$$