Question Number 178693 by peter frank last updated on 20/Oct/22 $$\mathrm{P}{rove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{tan}\:\mathrm{2x}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}+\mathrm{4cos}\:^{\mathrm{2}} \mathrm{x}}\:−\sqrt{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}+\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x}}}=\mathrm{1} \\ $$ Commented by peter frank…
Question Number 178692 by peter frank last updated on 20/Oct/22 $$\int\frac{\mathrm{tan}\:\left(\mathrm{ln}\:{x}\right).\mathrm{tan}\:\left(\mathrm{ln}\:\frac{{x}}{\mathrm{2}}\right).\mathrm{tan}\:\left(\mathrm{ln}\:\mathrm{2}\right)}{{x}}{dx} \\ $$$$ \\ $$ Answered by mindispower last updated on 21/Oct/22 $${tg}\left({ln}\left(\frac{{x}}{\mathrm{2}}\right)+{ln}\left(\mathrm{2}\right)\right)={tg}\left({lnx}\right)=\frac{{tg}\left({ln}\left[\left(\mathrm{2}\right)\right)+{tgg}\left({ln}\left(\frac{{x}}{\mathrm{2}}\right)\right)\right.}{\mathrm{1}−{tg}\left({ln}\left(\mathrm{2}\right)\right){tg}\left({ln}\left(\frac{{x}}{\mathrm{2}}\right)\right)} \\ $$$$\Leftrightarrow{tg}\left({ln}\left({x}\right)\right){tg}\left({ln}\left(\frac{{x}}{\mathrm{2}}\right)\right){tgln}\mathrm{2}=−{tgln}\left(\mathrm{2}\right)−{tgln}\frac{{x}}{\mathrm{2}}…
Question Number 113159 by Dwaipayan Shikari last updated on 11/Sep/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} {log}\left(\mathrm{1}−{x}\right){dx} \\ $$ Answered by MJS_new last updated on 11/Sep/20 $$\int{x}^{\mathrm{2}} \mathrm{ln}\:\left(\mathrm{1}−{x}\right)\:{dx}=…
Question Number 47595 by ajfour last updated on 12/Nov/18 Commented by ajfour last updated on 12/Nov/18 $${Regarding}\:{Q}.\mathrm{47497}\:\left({some}\:{analysis}\right) \\ $$$${Also}\:{see}\:{diagram}\:{of}\:{Q}.\mathrm{47599}\: \\ $$$${for}\:{part}\:{of}\:{solution}\left({section}\:{A}\right). \\ $$ Commented by…
Question Number 178657 by mnjuly1970 last updated on 19/Oct/22 $$ \\ $$$$\:\:\:\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\:\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{1}+\:\mathrm{tan}\left(\mathrm{2x}\right)}\:\mathrm{dx}\:=\:? \\ $$$$\: \\ $$ Terms of Service…
Question Number 113110 by gopikrishnan last updated on 11/Sep/20 $$\overset{\mathrm{1}} {\int}_{\mathrm{0}} \sqrt{{x}\left({x}−\mathrm{1}\right){dx}} \\ $$ Commented by 1549442205PVT last updated on 11/Sep/20 $$\mathrm{The}\:\mathrm{function}\:\sqrt{\mathrm{x}\left(\mathrm{x}−\mathrm{1}\right)}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{on} \\ $$$$\mathrm{set}\:\mathrm{X}=\left(−\infty,\mathrm{0}\right]\cup\left[\mathrm{1},+\infty\right)\:\mathrm{and}\:\mathrm{isn}'\mathrm{t} \\…
Question Number 113111 by gopikrishnan last updated on 11/Sep/20 $${find}\:{the}\:{area}\:{bounded}\:{by}\:{the}\:{curve}\:{y}^{\mathrm{2}} ={x}^{\mathrm{3}} \:{and}\:{the}\:{lines}\:{x}=\mathrm{0}\:{y}=\mathrm{1}\:{and}\:{y}=\mathrm{2} \\ $$ Answered by 1549442205PVT last updated on 11/Sep/20 $$\mathrm{y}^{\mathrm{2}} =\mathrm{x}^{\mathrm{3}} \Leftrightarrow\mathrm{y}=\sqrt{\mathrm{x}^{\mathrm{3}} }\:.\mathrm{We}\:\mathrm{find}\:\mathrm{the}…
Question Number 47566 by tanmay.chaudhury50@gmail.com last updated on 11/Nov/18 $$\int{sin}\mathrm{51}{x}\left({sinx}\right)^{\mathrm{49}} {dx} \\ $$ Answered by Smail last updated on 12/Nov/18 $${A}=\int{sin}\left(\mathrm{50}{x}+{x}\right){sin}^{\mathrm{49}} \left({x}\right){dx} \\ $$$$=\int\left({sin}\left(\mathrm{50}{x}\right){cosx}+{cos}\left(\mathrm{50}{x}\right){sin}\left({x}\right)\right){sin}^{\mathrm{49}} \left({x}\right){dx}…
Question Number 47540 by maxmathsup by imad last updated on 11/Nov/18 $${find}\:\int\:{arctan}\left(\sqrt{{x}}\right){dx}. \\ $$ Commented by maxmathsup by imad last updated on 16/Nov/18 $${let}\:{I}=\int\:{arctan}\left(\sqrt{{x}}\right){dx}\:{changement}\:\sqrt{{x}}={t}\:{give} \\…
Question Number 47527 by sandeepkeshari0797@gmail.com last updated on 11/Nov/18 Terms of Service Privacy Policy Contact: info@tinkutara.com