JEE PYQ: Definite Integration Question 6
Question 6 - 2021 (17 Mar Shift 2)
If the integral $\int_0^{10} \dfrac{[\sin 2\pi x]}{e^{x - [x]}},dx = \alpha e^{-1} + \beta e^{-\frac{1}{2}} + \gamma$, 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) $10$