Jee Main
Definite Integration
JEE Main 2022 (Online) 24th June Morning Shift
INTEGER+4 / -12022
ধর \(\mathop {Max}\limits_{0\, \le x\, \le \,2} \,\left\{ {{{9 - {x^2}} \over {5 - x}}} \right\} = \alpha\)
এবং \(\mathop {Min}\limits_{0\, \le x\, \le \,2} \,\left\{ {{{9 - {x^2}} \over {5 - x}}} \right\} = \beta\)
যদি \(\int\limits_{\beta - {8 \over 3}}^{2\alpha - 1} {} Max\,\left\{ {{{9 - {x^2}} \over {5 - x}},x} \right\}dx = {\alpha _1} + {\alpha _2}{\log _e}\left( {{8 \over {15}}} \right)\) হয়, তাহলে \({\alpha _1} + {\alpha _2}\) = ______
এবং \(\mathop {Min}\limits_{0\, \le x\, \le \,2} \,\left\{ {{{9 - {x^2}} \over {5 - x}}} \right\} = \beta\)
যদি \(\int\limits_{\beta - {8 \over 3}}^{2\alpha - 1} {} Max\,\left\{ {{{9 - {x^2}} \over {5 - x}},x} \right\}dx = {\alpha _1} + {\alpha _2}{\log _e}\left( {{8 \over {15}}} \right)\) হয়, তাহলে \({\alpha _1} + {\alpha _2}\) = ______