If the value of the integral \stackrel{5}{\\int}_{0} \frac{x+[x]}{e^{x-[x]}} d x= \alphae^{-}+\\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: [26 Aug 2021 Shift 2]

JEE Main 26-Aug-2021 Shift 2 Solved Paper

Section: Mathematics

Question : 64 of 90

Marks: +1, -0

If the value of the integral

∫

‌

x+[x]

ex−[x]

dx=αe−+β, where α,β∈R,5α+6β=0 and [x] denotes the greatest integer less than or equal to x, then the value of (α+β)2 is equal to:

[26 Aug 2021 Shift 2]

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