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Author: Tinku Tara

ln-sinx-dx-

Question Number 154673 by Study last updated on 20/Sep/21 $$\int{ln}\left({sinx}\right){dx}=? \\ $$ Commented by puissant last updated on 20/Sep/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({sinx}\right){dx}=−\frac{\pi}{\mathrm{2}}{ln}\mathrm{2}.. \\ $$ Commented…

how-many-positive-x-10-000-integers-are-such-that-2-x-x-2-is-divisible-by-7-

Question Number 154672 by talminator2856791 last updated on 20/Sep/21 $$\: \\ $$$$\:\mathrm{how}\:\mathrm{many}\:\mathrm{positive}\:{x}\leqslant\mathrm{10}\:\mathrm{000}\:\mathrm{integers}\:\mathrm{are}\:\: \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{2}^{{x}} −{x}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{7}? \\ $$$$\: \\ $$ Answered by MJS_new last updated…

if-we-let-f-n-n-2-n-1-then-solve-the-equation-for-real-numbers-f-f-f-f-n-1-32-

Question Number 154675 by mathdanisur last updated on 20/Sep/21 $$\mathrm{if}\:\mathrm{we}\:\mathrm{let} \\ $$$$\mathrm{f}\left(\mathrm{n}\right)\:=\:\frac{\mathrm{n}}{\mathrm{2}}\:\left(\mathrm{n}\:+\:\mathrm{1}\right) \\ $$$$\mathrm{then}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{n}\right)\right)\right)\right)\:=\:\frac{\mathrm{1}}{\mathrm{32}} \\ $$ Answered by MJS_new last updated on 20/Sep/21…

Question-154669

Question Number 154669 by SANOGO last updated on 20/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 20/Sep/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dt}}{\:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }+\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}} \left(\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }−\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }\right){dt}…

If-f-x-f-x-1-f-x-1-where-f-10-6-and-f-20-2f-21-then-f-16-

Question Number 154668 by EDWIN88 last updated on 20/Sep/21 $$\:{If}\:{f}\left({x}\right)={f}\left({x}−\mathrm{1}\right)+{f}\left({x}+\mathrm{1}\right)\:{where} \\ $$$${f}\left(\mathrm{10}\right)=\mathrm{6}\:{and}\:{f}\left(\mathrm{20}\right)=\mathrm{2}{f}\left(\mathrm{21}\right) \\ $$$${then}\:{f}\left(\mathrm{16}\right)=\ldots? \\ $$ Commented by mathdanisur last updated on 20/Sep/21 $$\mathrm{f}\left(\mathrm{16}\right)\:=\:-\:\mathrm{f}\left(\mathrm{21}\right) \\…