$\int\limits_0^∞[2 e^{-x}]dx$, where [.] denotes the greatest integer function, is equal to
Answer & explanation
Correct answer: option 2
Since 0 < 2e-x ≤ 2 ∀x ∈ [0 , ∞),
[2e-x] = 0, for x > ln 2.
Hence the given integral = $\int\limits_0^{In\,2}dx+0=In\,2$.
Hence (B) is the correct answer.