Question

AM 185 Culegere UPT.

Am ajuns intr-un punct de unde nu mai stiu ce sa fac. Cum ar trebui sa continui?

Answer 1

$\text{x tinde la } \dfrac{\pi}{2} \text{ cand }x < \dfrac{\pi}{2}. \\ \\ \text{Deoarece domeniul nostru de integrare porneste de la 0 si }\\ \text{se termina la }\pi.\\ \text{Deci, traseul lui e prin stanga lui}~\dfrac{\pi}{2}.\\ \\ \Rightarrow \dfrac{2}{3}\cdot \arctan\Big(3\tan(\frac{\pi}{2})\Big) = \lim\limits_{x\to \frac{\pi}{2}, x<\frac{\pi}{2}} \dfrac{2}{3}\arctan\big(3\tan(x)\big) = \\ \\ = \dfrac{2}{3}\arctan(3\cdot \infty) =\dfrac{2}{3} \arctan( \infty) = \\ \\ = \dfrac{2}{3}\cdot \dfrac{\pi}{2} = \dfrac{\pi}{3}$

Answer 2

Se foloseste o integrala improprie, - Flondor, Donciu -432 .