Question Number 136076 by physicstutes last updated on 18/Mar/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:\mathrm{3}\:+\:\mathrm{2}{x}\:−{x}^{\mathrm{2}} ,\:\mathrm{the}\:{x}−\mathrm{axis} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{line}\:{y}\:=\:\mathrm{3}. \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solid}\:\mathrm{generated}\:\mathrm{when}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{is} \\ $$$$\mathrm{rotated}\:\mathrm{completely}\:\mathrm{about}\:\mathrm{the}\:\mathrm{line}\:{y}\:=\:\mathrm{3} \\ $$ Answered by mr W last updated…
Question Number 136067 by bramlexs22 last updated on 18/Mar/21 $$\Lambda\:=\:\int\:{x}^{\mathrm{3}} \:\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{10}} \:{dx}\: \\ $$ Answered by Olaf last updated on 18/Mar/21 $$\Lambda\:=\:\int{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{10}}…
Question Number 136060 by mnjuly1970 last updated on 18/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:\:{evaluate}:: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\mathrm{Im}\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {li}_{\mathrm{2}} \left({sin}\left({x}\right)\right)+{li}_{\mathrm{2}} \left({csc}\left({x}\right)\right){dx}\right) \\ $$$$ \\ $$ Answered by mindispower…
Question Number 136036 by mathmax by abdo last updated on 18/Mar/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{logx}}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$ Commented by Ajetunmobi last updated on 18/Mar/21…
Question Number 136034 by mathmax by abdo last updated on 18/Mar/21 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$$$ \\ $$ Answered by mathmax by abdo…
Question Number 4957 by ankit chakravarti last updated on 26/Mar/16 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{4}{x}^{\mathrm{3}} \left\{\frac{{d}^{\mathrm{2}} }{{dx}^{\mathrm{2}} }\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{5}} \right\}{dx}=? \\ $$ Commented by ankit chakravarti last…
Question Number 136023 by mathmax by abdo last updated on 18/Mar/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{z}^{\mathrm{2}} } \mathrm{dz}\:\:\mathrm{with}\:\mathrm{z}\:\mathrm{complex} \\ $$ Commented by yutytfjh67ihd last updated on 25/Mar/21…
Question Number 70482 by Mikaell last updated on 04/Oct/19 $$\int\frac{{sin}^{\mathrm{3}} {x}}{\:\sqrt{{cosx}}}{dx} \\ $$ Commented by kaivan.ahmadi last updated on 04/Oct/19 $${u}={cosx}\Rightarrow{du}=−{sinxdx} \\ $$$${sin}^{\mathrm{3}} {x}={sinxsin}^{\mathrm{2}} {x}={sinx}\left(\mathrm{1}−{cos}^{\mathrm{2}}…
Question Number 70483 by Mikaell last updated on 04/Oct/19 $$\int\frac{{ln}\mathrm{2}{x}}{{ln}\mathrm{4}{x}}.\frac{{dx}}{{x}} \\ $$ Commented by peter frank last updated on 04/Oct/19 $${thankx} \\ $$ Commented by…
Question Number 135996 by mnjuly1970 last updated on 17/Mar/21 Answered by Dwaipayan Shikari last updated on 17/Mar/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}+\mathrm{1}} }{{n}^{\mathrm{2}} }{dx} \\…