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Integral Calculus> Please solve this integral ∫(2 x /2 [x]) ...

question mark

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

Lovey , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 11 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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