If the integral ∫ (|sin 2 πx|)/(e^(e - |x|))dx x ∈ [0, 10] = αe^(-1) + βe^(1/2) + γ, where α, β, γ are integers

Question

If the integral \(\int\limits_0^{10}\frac{[sin\,2\,\pi x]}{e^{e-[x]}}dx = \alpha e^{-1} + \beta e^\frac{1}{2}+\gamma,\) where \(\alpha, \beta, \gamma\) are integers and [x] denotes the greatest integer less than or equal to x, then the value of \(\alpha + \beta + \gamma\) is equal to :

(1) 0

(2) 20

(3) 25

(4) 10

Answer 1

Answer is (1)