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Question Number 205315 by cherokeesay last updated on 15/Mar/24

Answered by MM42 last updated on 16/Mar/24

$$\left[x\right]+[x-\frac{1}{2}]=\left[2x\right]-1$$$$\Rightarrow {\int }_0^{\left[x\right]}(\left[2x\right]-1)dx=(\left[2x\right]-1)x{\mid }_0^{\left[x\right]}$$$$=(\left[2x\right]-1)\left[x\right]$$$$\Rightarrow {\int }_0^{\left[x\right]}\left({\int }_0^{\left[x\right]}(\left[2x\right]-1)\left[x\right]\right))dx$$$$=(\left[2x\right]-1){\left[x\right]}^2✓$$$$$$

Commented by cherokeesay last updated on 16/Mar/24

$$thankyou!$$

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