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Find the integral, limit ( 0 to infinity) ∫[2e -x ] dx [] isintegral part function

Find the integral, limit ( 0  to infinity)
∫[2e-x] dx
[] isintegral part function

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:Hello student, please find answer to your question
I = \int_{0}^{\infty }[2e^{-x}]dx
Since
0 < [2e^{-x}] \leq 2, \forall x\in [0, \infty )
[2e^{-x}] = 1 , 0 < x < ln2
[2e^{-x}] = 0 , \forall x > ln2
Hence,
I =\int_{0}^{ln2}1.dx + \int_{ln2}^{\infty }0.dx
I = [x]_{0}^{ln2}
I = {ln2}

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