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Question Number 207352 by NasaSara last updated on 12/May/24

$$calculate:$$$${\int }_{\frac{\mathrm{\Pi }}{4}}^{\frac{\mathrm{\Pi }}{2}}\lfloor cot\left(x\right)\rfloor dx$$

Commented by NasaSara last updated on 12/May/24

$$thankyou$$

Commented by Berbere last updated on 12/May/24

$$withePleasur$$

Commented by Berbere last updated on 12/May/24

$$0⩽cot\left(x\right)<1;\mathrm{\forall }x\in ]\frac{\pi }{4};\frac{\pi }{2}]\Rightarrow \left[cot\left(x\right)\right]=0$$$${\int }_{\frac{\pi }{4}}^{\frac{\pi }{2}}\left[cot\left(x\right)\right]dx=0$$

Answered by MM42 last updated on 12/May/24

$$\frac{\pi }{4}<x<\frac{\pi }{2}\Rightarrow 0<cotx<1\Rightarrow \lfloor cotx\rfloor =0$$$$\Rightarrow I=0✓$$

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