limite cu integrale improrii

[Cezar Lupu]

Sa se calculeze urmatoarele limite:

i) \( \lim_{n\to\infty}\int_0^{(2n+1)\frac{\pi}{2}}\sin t \log\frac{1}{t}dt \);

ii) \( \lim_{n\to\infty}\int_0^{n\pi}\cos t \log\frac{1}{t}dt \).

American Mathematical Monthly