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
Question Number 178563 by zaheen last updated on 18/Oct/22 $$\int{e}^{{x}^{\mathrm{2}} } {dx}=? \\ $$ Answered by Acem last updated on 18/Oct/22 $$ \\ $$$${We}\:{have}\:\int{e}^{−{x}^{\mathrm{2}} }…
Question Number 178550 by cortano1 last updated on 18/Oct/22 Answered by Ar Brandon last updated on 18/Oct/22 $${I}=\int_{\frac{\pi}{\mathrm{12}}} ^{\frac{\pi}{\mathrm{8}}} \frac{\left(\mathrm{7}+\mathrm{cos4}\vartheta\right)\mathrm{cos2}\vartheta}{\mathrm{1}−\mathrm{cos4}\vartheta}\left(\frac{\mathrm{9}−\mathrm{cos4}\vartheta}{\mathrm{sin2}\vartheta}\right)^{\mathrm{2021}} {d}\vartheta \\ $$$$\:\:=\int_{\frac{\pi}{\mathrm{12}}} ^{\frac{\pi}{\mathrm{8}}} \frac{\left(\mathrm{6}+\mathrm{2cos}^{\mathrm{2}}…
Question Number 113004 by malwan last updated on 10/Sep/20 $${prove}\:{that} \\ $$$$\:_{\mathrm{0}} \int^{\:\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}\:=\:\:_{\mathrm{0}} \int^{\:\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}\:=\frac{\sqrt{\pi}}{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$ Answered by mathdave last updated…