Question: $\int_{0}^{\infty}{}$ [2 e<sup>-x</sup>]dx, where [.] denotes the greatest integer function, is eq...

Question

$\int_{0}^{\infty}{}$ [2 e^-x]dx, where [.] denotes the greatest integer function, is equal to

Answer 1

Since 0 < 2 e^–x ≤ 2 ∀ x ∈ [0, ∞),

[2 e^–x] = 0, for x > ln2.

Hence the given integral = $\int_{0}^{ln2}{dx}$ + 0 = ln 2

Question: \(\int_{0}^{\infty}{}\) [2 e<sup>-x</sup>]dx, where [.] denotes the greatest integer function, is eq...