Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationProperties of definite integrationEasy2 min

MathematicsEasysingle choice

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

Answer:

Solution:

Since $0 < 2 e^{- x} \leq 2$ for all $x \in [0, \infty)$ , we have $⌊ 2 e^{- x} ⌋ = 0$ for $x > ln 2$ . Hence, the given integral is:

$\int_{0}^{l n 2} d x + 0 = ln 2$

Therefore, (B) is the correct answer.

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Properties of definite integration

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