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Integral and Riemann sum limit computation

1925SpecialistCalculusSeries

Olimpiada Naţională de Matematică

a. Compute: $$ \int_{0}^{1} x \sin \left(\pi x^{2}\right) \mathrm{d} x $$ b. Compute: $$ \lim _{n \rightarrow \infty} \frac{1}{n} \sum_{k=0}^{n-1} k \int_{\frac{k}{n}}^{\frac{k+1}{n}} \sin \left(\pi x^{2}\right) \mathrm{d} x $$
0 students attempted0% solvedRating 1925

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