Suma Riemann sau poate nu!

[Theodor Munteanu]

Calculati:
\( {\lim }\limits_{t \to \infty } \int\limits_0^t {\frac{1}{{\left( {x^2 + 1} \right)\left( {x^2 + 4} \right)\left( {x^2 + 9} \right) \ldots \left( {x^2 + n^2 } \right)}}dx} \)

[Marius Mainea]

Cu schimbarea de variabila \( x=\tan y \) se obtine ca limita este \( \int_0^{\frac{\pi}{2}}\frac{\cos^{2(n-1)}y}{(4\cos^2y+\sin^2y)(9\cos^2y+\sin^2y)....(n^2\cos^2y+\sin^2y)}dy \)