pi ∫ (from 1 to e) of (Q_n^y)^2 wrt y ಪರಿಹರಿಸಿ

$$\pi \int _ { 1 } ^ { e } ( Q _ { n } ^ { y } ) ^ { 2 } d y$$

ಮೌಲ್ಯಮಾಪನ

$$\left\{\begin{matrix}\frac{\pi \left(Q_{n}^{2e}-Q_{n}^{2}\right)}{2\ln(Q_{n})},&Q_{n}>0\text{ and }Q_{n}\neq 1\\\pi \left(e-1\right),&Q_{n}=1\end{matrix}\right.$$

ವ್ಯತ್ಯಾಸ w.r.t. Q_n

$$\left\{\begin{matrix}\frac{\pi \left(2eQ_{n}^{2e}\ln(Q_{n})-2Q_{n}^{2}\ln(Q_{n})-Q_{n}^{2e}+Q_{n}^{2}\right)}{2Q_{n}\ln(Q_{n})^{2}},&Q_{n}>0\text{ and }Q_{n}\neq 1\\0,&Q_{n}=1\end{matrix}\right.$$