Jee Main
Definite Integration
JEE Main 2021 (Online) 26th August Evening Shift
MCQ+4 / -12021
If the value of the integral
\(\int\limits_0^5 {{{x + [x]} \over {{e^{x - [x]}}}}dx = \alpha {e^{ - 1}} + \beta }\), where \(\alpha\), \(\beta\) \(\in\) R, 5\(\alpha\) + 6\(\beta\) = 0, and [x] denotes the greatest integer less than or equal to x; then the value of (\(\alpha\) + \(\beta\))2 is equal to :
\(\int\limits_0^5 {{{x + [x]} \over {{e^{x - [x]}}}}dx = \alpha {e^{ - 1}} + \beta }\), where \(\alpha\), \(\beta\) \(\in\) R, 5\(\alpha\) + 6\(\beta\) = 0, and [x] denotes the greatest integer less than or equal to x; then the value of (\(\alpha\) + \(\beta\))2 is equal to :