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Please solve this integral ∫(2 x /2 [x]) dx [] is the integral part of x. Limit if from 0 to 100.

Please solve this integral
∫(2x/2[x]) dx
[] is the integral part of x.
Limit if from 0 to 100.

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int_{0}^{100}\frac{2^x}{2^{[x]}}dx
I = \int_{0}^{100}2^{x-[x]}dx
I = \int_{0}^{100}2^{(x)}dx
() is fractional part of and its time of period is 1. So
I = 100\int_{0}^{1}2^{x}dx
I = 100.(\frac{2^{x}}{ln2})_{0}^{1}
I = 100.(\frac{2-1}{ln2})
I = \frac{100}{ln2}

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