Question Number 87298 by ajfour last updated on 03/Apr/20 $${If}\:{y}=\mathrm{sin}\:{x}\:,\:\:{x}=\mathrm{0}\:{to}\:{x}=\mathrm{2}\pi\:{is} \\ $$$${revolved}\:{about}\:{the}\:{x}-{axis},\:{find} \\ $$$${the}\:{surface}\:{of}\:{the}\:{solid}\:{of} \\ $$$${revolution}. \\ $$ Answered by ajfour last updated on 04/Apr/20…
Question Number 87279 by Ar Brandon last updated on 03/Apr/20 $$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$ Commented by abdomathmax last updated on 03/Apr/20 $${complex}\:{method}\:\:{let}\:{decompose}\:{F}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} \:+\mathrm{1}}…
Question Number 21721 by Isse last updated on 02/Oct/17 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {sin}^{\mathrm{2}} {xcos}^{\mathrm{3}} {xdx} \\ $$ Answered by sma3l2996 last updated on 02/Oct/17 $$=\int_{\mathrm{0}} ^{\pi/\mathrm{2}}…
Question Number 21720 by Isse last updated on 01/Oct/17 $$\int{sin}^{\mathrm{5}} \theta{d}\theta \\ $$ Answered by sma3l2996 last updated on 02/Oct/17 $$=\int\left(\mathrm{1}−{cos}^{\mathrm{2}} {x}\right)^{\mathrm{2}} {sinxdx}=\int\left({sinx}−\mathrm{2}{sinxcos}^{\mathrm{2}} {x}+{sinxcos}^{\mathrm{4}} {x}\right){dx}…
Question Number 21708 by Isse last updated on 01/Oct/17 $$\int_{\mathrm{0}} ^{\mathrm{0}.\mathrm{5}} \mathrm{2}{tan}^{\mathrm{2}} \mathrm{2}{tdt} \\ $$ Answered by $@ty@m last updated on 01/Oct/17 $$\int_{\mathrm{0}} ^{\mathrm{0}.\mathrm{5}} \mathrm{2}\left(\mathrm{sec}\:^{\mathrm{2}}…
Question Number 21707 by Isse last updated on 01/Oct/17 $$\int_{\pi/\mathrm{6}} ^{\pi/\mathrm{3}} \frac{\mathrm{1}}{\mathrm{2}}{cot}^{\mathrm{2}} \mathrm{2}\theta{d}\theta \\ $$ Commented by Tikufly last updated on 01/Oct/17 $$\mathrm{I}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\pi/\mathrm{6}} ^{\pi/\mathrm{3}} \left(\mathrm{cosec}^{\mathrm{2}}…
Question Number 152778 by mnjuly1970 last updated on 01/Sep/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Solve}\:………. \\ $$$$\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}.\:{sin}\left(\:{ln}\:\left({x}\:\right)\right){dx}\:\overset{?} {=}\:\frac{−\mathrm{1}}{\:\:\:\mathrm{5}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{solution}…. \\ $$$$\:\:\:\:\:\Omega\::\overset{{i}.{b}.{p}} {=}\left[\:\frac{{x}^{\:\mathrm{2}} }{\mathrm{2}}\:.\:{sin}\left({ln}\left({x}\right)\right)\right]_{\mathrm{0}} ^{\:\mathrm{1}} −\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}}…
Question Number 21701 by Isse last updated on 01/Oct/17 $$\int\mathrm{2}{cot}^{\mathrm{2}} \mathrm{2}{t} \\ $$ Commented by Tikufly last updated on 01/Oct/17 $$\mathrm{I}\:\mathrm{think}\:\mathrm{your}\:\mathrm{question}\:\mathrm{should} \\ $$$$\mathrm{be}\:\int\mathrm{2cot}^{\mathrm{2}} \mathrm{2tdt} \\…
Question Number 21702 by Isse last updated on 01/Oct/17 $$\int_{\pi/\mathrm{6}} ^{\pi/\mathrm{3}} \mathrm{1}/\mathrm{2}{cot}^{\mathrm{2}} \mathrm{2}\theta{d}\theta \\ $$ Commented by Tikufly last updated on 01/Oct/17 $$\int_{\pi/\mathrm{6}} ^{\pi/\mathrm{3}} \frac{\mathrm{1}}{\mathrm{2}{cot}^{\mathrm{2}}…
Question Number 21679 by Arnab Maiti last updated on 30/Sep/17 $$\int\frac{\mathrm{sec}\theta\:\mathrm{d}\theta}{\mathrm{1}−\mathrm{sec}\theta} \\ $$ Answered by alex041103 last updated on 30/Sep/17 $${First}\:{we}\:{make}\:{the}\:{following}\:{transformations}: \\ $$$$\int\frac{\mathrm{sec}\theta\:\mathrm{d}\theta}{\mathrm{1}−\mathrm{sec}\theta}=\int\frac{\frac{\mathrm{1}}{{cos}\theta}}{\mathrm{1}−\frac{\mathrm{1}}{{cos}\theta}}{d}\theta= \\ $$$$=\int\frac{\frac{\mathrm{1}}{{cos}\theta}}{\mathrm{1}−\frac{\mathrm{1}}{{cos}\theta}}\:\frac{{cos}\theta}{{cos}\theta}{d}\theta=…