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Author: Tinku Tara

1-2-1-x-2-sin-1-x-dx-

Question Number 17008 by arnabpapu550@gmail.com last updated on 29/Jun/17 $$\int_{\frac{\mathrm{1}\:}{\Pi}} ^{\frac{\mathrm{2}}{\Pi}} \:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\mathrm{sin}\frac{\mathrm{1}}{\mathrm{x}}\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 29/Jun/17 $${t}=\frac{\mathrm{1}}{{x}}\Rightarrow{dt}=\frac{−{dx}}{{x}^{\mathrm{2}} } \\…

cos-n-x-sinx-dx-

Question Number 148077 by mathdanisur last updated on 25/Jul/21 $$\int\:\frac{{cos}^{\boldsymbol{{n}}} {x}}{{sinx}}\:{dx}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 26/Jul/21 $$\mathrm{I}_{{n}} \left({x}\right)\:=\:\int\frac{\mathrm{cos}^{{n}} {x}}{\mathrm{sin}{x}}\:{dx} \\ $$$$…

Lim-x-4x-2-8x-3-2x-4-

Question Number 82541 by zainal tanjung last updated on 22/Feb/20 $$\:\underset{\mathrm{x}\rightarrow\infty} {\mathrm{Lim}}\:\sqrt{\mathrm{4x}^{\mathrm{2}} −\mathrm{8x}+\mathrm{3}}\:−\mathrm{2x}−\mathrm{4} \\ $$ Commented by john santu last updated on 22/Feb/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{4}{x}^{\mathrm{2}}…

Question-148068

Question Number 148068 by tabata last updated on 25/Jul/21 Answered by Olaf_Thorendsen last updated on 25/Jul/21 $$\left(\mathrm{B}\right) \\ $$$$\mathrm{Let}\:{f}\left({z}\right)\:=\:{z}^{\mathrm{7}} −\mathrm{4}{z}^{\mathrm{3}} +{z}−\mathrm{1}\:=\:\mathrm{0},\:\mid{z}\mid\:=\:\mathrm{1} \\ $$$$\mathrm{and}\:{g}\left({z}\right)\:=\:−\mathrm{4}{z}^{\mathrm{3}} \\ $$$$…

Question-82531

Question Number 82531 by Power last updated on 22/Feb/20 Commented by abdomathmax last updated on 24/Feb/20 $${I}\:=\int\:\frac{\sqrt{\mathrm{1}−{x}}}{{x}}{dx}\:+\int\:\frac{\sqrt{\mathrm{2}−{x}^{\mathrm{2}} }}{{x}}{dx}\:+\int\:\:\frac{\sqrt{\mathrm{4}−{x}^{\mathrm{4}} }}{{x}}{dx}\:{we}\:{have} \\ $$$$\int\:\:\frac{\sqrt{\mathrm{1}−{x}}}{{x}}{dx}\:\:{changement}\:\sqrt{\mathrm{1}−{x}}={t}\:{give}\mathrm{1}−{x}={t}^{\mathrm{2}} \:\Rightarrow \\ $$$${x}=\mathrm{1}−{t}^{\mathrm{2}} \:\Rightarrow\int\:\:\frac{\sqrt{\mathrm{1}−{x}}}{{x}}{dx}\:=\:\int\:\:\frac{{t}}{\mathrm{1}−{t}^{\mathrm{2}}…

If-for-positive-integers-a-and-b-a-b-a-b-b-a-find-a-2-b-2-

Question Number 16990 by 1234Hello last updated on 29/Jun/17 $$\mathrm{If}\:\mathrm{for}\:\mathrm{positive}\:\mathrm{integers}\:{a}\:\mathrm{and}\:{b}, \\ $$$${a}\:+\:{b}\:=\:\frac{{a}}{{b}}\:+\:\frac{{b}}{{a}},\:\mathrm{find}\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} . \\ $$ Commented by RasheedSoomro last updated on 29/Jun/17 $${a}\:+\:{b}\:=\:\frac{{a}}{{b}}\:+\:\frac{{b}}{{a}} \\…