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The value of $\int_{0}^{[x]} \frac{2^{t}}{2^{[t]}} d t$ (where [ ] denotes greatest integer function)

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Correct option is B

I=∫0[x] 2t2[t]dt=∫0[x] 2t−[t]dtThe function g(t)=2t−[t] is periodic with period 1, ThereforeI=[x]∫01 2t−[t]dt=[x]∫01 2tdt=[x]log⁡2[2t]01=[x]log⁡2

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The value of ∫0[x] 2t2[t]dt(where [ ] denotes greatest integer function)

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The value of $\int_{0}^{[x]} \frac{2^{t}}{2^{[t]}} d t$ (where [ ] denotes greatest integer function)