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Definite Integration question

2021 · 26 Aug · Shift 2 · Q26
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  5. /2021 · 26 Aug · Shift 2 · Q26

Definite Integration question

2021 · 26 Aug · Shift 2 · Q26

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1
If the value of the integral ∫05x+[x]ex−[x]dx=αe−1+β\int\limits_0^5 {{{x + [x]} \over {{e^{x - [x]}}}}dx = \alpha {e^{ - 1}} + \beta }0∫5​ex−[x]x+[x]​dx=αe−1+β, where α\alphaα, β∈\beta\inβ∈ R, 5 α\alphaα + 6 β\betaβ = 0, and [x] denotes the greatest integer less than or equal to x; then the value of (α\alphaα+β\betaβ)2 is equal to :
  1. A
    100
  2. B
    25
  3. C
    16
  4. D
    36
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