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Question Number 51995 by maxmathsup by imad last updated on 01/Jan/19

$$letfdefinedon[0,1]byf\left(0\right)=0andf\left(x\right)=\frac{1}{2\left[\frac{1}{2x}\right]+1}$$$$calculate{\int }_0^{1}f\left(x\right)dx$$

Answered by tanmay.chaudhury50@gmail.com last updated on 03/Jan/19

$$x\frac{1}{x}\frac{1}{2x}\left[\frac{1}{2x}\right]2\left[\frac{1}{2x}\right]+1\frac{1}{2\left[\frac{1}{2x}\right]+1}$$$$1.010.5011$$$$0.91.110.55011$$$$.....$$$$0.511.960.98011$$$$0.52113\frac{1}{3}$$$$0.42.51.2513\frac{1}{3}$$$$0.33.331.6713\frac{1}{3}$$$$0.252.525\frac{1}{5}$$$$$$$$$$$$$$$${\int }_0^1\frac{1}{2\left[\frac{1}{2x}\right]+1}dx$$$$+{\int }_{0.2}^{0.3}\frac{1}{5}+{\int }_{0.3}^{0.5}\frac{1}{3}dx+{\int }_{0.5}^{1}1dx$$$$wait...$$

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