Question Number 168852 by bagjagugum123 last updated on 19/Apr/22 Commented by CAIMAN last updated on 19/Apr/22 3π/8 Commented by safojontoshtemirov last updated on 20/Apr/22 $${solution}.{Safojon}.{Toshtemirov}.…
Question Number 103312 by bemath last updated on 14/Jul/20 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{6}} }\:{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 14/Jul/20 $$\int_{\mathrm{0}}…
Question Number 37777 by rahul 19 last updated on 17/Jun/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{curves}\:\mathrm{9}{x}^{\mathrm{2}} +\mathrm{9}{y}^{\mathrm{2}} −\mathrm{30}{y}+\mathrm{16}=\mathrm{0}\:{and} \\ $$$${y}^{\mathrm{2}} ={x}^{\mathrm{3}} \:. \\ $$ Answered by MJS last…
Question Number 168828 by infinityaction last updated on 18/Apr/22 $$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2cos}\:{x}}\right){dx} \\ $$ Commented by infinityaction last updated on 18/Apr/22 $${please}\:{solve}\:{this}\:{problem}…
Question Number 168812 by infinityaction last updated on 18/Apr/22 $$\int_{\mathrm{0}} ^{\pi} \left(\mathrm{sin}\:{x}\right)^{\mathrm{cos}\:{x}} {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 103241 by Dwaipayan Shikari last updated on 13/Jul/20 $$\int{x}^{−{x}} {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 168772 by Dildora last updated on 17/Apr/22 Commented by safojontoshtemirov last updated on 18/Apr/22 $${S}=\mathrm{4}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\sqrt{\left(\left({e}^{{t}} {sint}\right)'\right)^{\mathrm{2}} +\left(\left({e}^{{t}} {cost}\right)'\right)^{\mathrm{2}} }{dt}\: \\ $$$${S}=\mathrm{4}\underset{\mathrm{0}}…
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Question Number 168762 by Dildora last updated on 17/Apr/22 Commented by cortano1 last updated on 17/Apr/22 $$\:\int\:\frac{\mathrm{2sin}\:\frac{\mathrm{1}}{\mathrm{2}}{x}\:\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}{x}}{\mathrm{2cos}\:\frac{\mathrm{1}}{\mathrm{2}}{x}\left(\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{x}\right)}\:{dx} \\ $$$$\:=\:\int\:\frac{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{x}}{\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{x}}\:{dx} \\ $$$$\:=\:\int\:\frac{\mathrm{2sin}\:{u}}{\mathrm{cos}\:{u}+\mathrm{sin}\:{u}}\:{du}\:;\:\left[\frac{\mathrm{1}}{\mathrm{2}}{x}={u}\:\right] \\ $$$$\frac{\mathrm{2sin}\:{u}}{\mathrm{cos}\:{u}+\mathrm{sin}\:{u}}\:=\:{A}\left(\frac{\mathrm{sin}\:{u}+\mathrm{cos}\:{u}}{\mathrm{sin}\:{u}+\mathrm{cos}\:{u}}\right)+{B}\left(\frac{{d}\left(\mathrm{sin}\:{u}+\mathrm{cos}\:{u}\right)}{\mathrm{sin}\:{u}+\mathrm{cos}\:{u}}\right) \\ $$$$\Rightarrow\mathrm{2sin}\:{u}=\:{A}\mathrm{sin}\:{u}+{A}\mathrm{cos}\:{u}+{B}\mathrm{cos}\:\:{u}−{B}\mathrm{sin}\:{u}…
Question Number 103220 by Dwaipayan Shikari last updated on 13/Jul/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{{e}^{{x}} +\mathrm{1}}{dx} \\ $$ Answered by mathmax by abdo last updated on…