If the value of the integral ∫₀⁵ (x + [x])/(e^(x - [x]))dx = α e⁻¹ + β, where α, β R, 5 α + 6 β = 0, and [x] denotes the greatest integer less than or equal to x; then the value of (α + β)² is equal to:

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 26 Aug, Evening shift · Q3417

JEE Main 202126 Aug, Evening shiftMathematicsHardIntegral Calculus369× since 2002

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 :

JEE Main 2021 Integral Calculus Question with Solution (26 Aug Evening shift, Q3417) | JEE Arc