Menu Close

Category: Integration

find-the-area-bounded-by-the-curve-y-2-x-3-and-the-lines-x-0-y-1-and-y-2-

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}…

sin51x-sinx-49-dx-

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-178550

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}}…

tan-x-dx-sec-3-x-1-

Question Number 112997 by malwan last updated on 10/Sep/20 $$\int\frac{\:{tan}\:{x}\:{dx}}{\:\sqrt{{sec}^{\mathrm{3}} \:{x}\:+\:\mathrm{1}}}\:=\:? \\ $$ Commented by MJS_new last updated on 10/Sep/20 $$\mathrm{sorry}\:\mathrm{I}\:\mathrm{haven}'\mathrm{t}\:\mathrm{got}\:\mathrm{the}\:\mathrm{time}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{it}\:\mathrm{but} \\ $$$$\mathrm{the}\:\mathrm{path}\:\mathrm{is} \\ $$$$\int\frac{\mathrm{tan}\:{x}}{\:\sqrt{\mathrm{sec}^{\mathrm{3}}…

dx-cot-3-x-sin-7-x-

Question Number 178487 by cortano1 last updated on 17/Oct/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{{dx}}{\mathrm{cot}\:^{\mathrm{3}} {x}\:\mathrm{sin}\:^{\mathrm{7}} {x}}\:=? \\ $$ Answered by Frix last updated on 18/Oct/22 $$\int\frac{{dx}}{\mathrm{cot}^{\mathrm{3}} \:{x}\:\mathrm{sin}^{\mathrm{7}} \:{x}}=\int\frac{{dx}}{\mathrm{cos}^{\mathrm{3}} \:{x}\:\mathrm{sin}^{\mathrm{4}}…