Question Number 71750 by TawaTawa last updated on 19/Oct/19 $$\int\:\mathrm{cos}^{\mathrm{3}} \theta\:\left(\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{3}} \theta\right) \\ $$$$\mathrm{Using}\:\mathrm{beta}\:\mathrm{function} \\ $$ Commented by mathmax by abdo last updated on 20/Oct/19…
Question Number 71751 by olalekan2 last updated on 19/Oct/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6214 by sanusihammed last updated on 18/Jun/16 $$\int\sqrt{{tanx}}\:\:{dx}\: \\ $$ Commented by nburiburu last updated on 24/Jun/16 $${by}\:\:{substitution} \\ $$$${t}=\sqrt{{tan}\:{x}}\Rightarrow{t}^{\mathrm{2}} =\:{tan}\:{x} \\ $$$$\mathrm{2}{t}\:{dt}\:=\:{sec}^{\mathrm{2}}…
Question Number 137280 by mathlove last updated on 31/Mar/21 Answered by EDWIN88 last updated on 31/Mar/21 $$\Leftrightarrow\:\mathrm{y}\:=\:\mathrm{x}^{\left(\frac{\pi}{\mathrm{ln}\:\mathrm{x}}\right)} =\:\mathrm{x}^{\pi\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{e}\right)} \\ $$$$\Leftrightarrow\:\mathrm{y}=\:\mathrm{x}^{\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{e}^{\pi} \right)} \:;\:\mathrm{y}\:=\:\mathrm{e}^{\pi} \:\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{0}.…
Question Number 137282 by mathlove last updated on 31/Mar/21 Answered by EDWIN88 last updated on 31/Mar/21 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{fofofof}\right)\left(\mathrm{x}\right)=\mathrm{f}\:'\left(\mathrm{x}\right)\mathrm{f}\:'\left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{f}\:'\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right)\:\mathrm{f}\:'\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right)\right) \\ $$ Answered by floor(10²Eta[1]) last updated on…
Question Number 137277 by mnjuly1970 last updated on 31/Mar/21 $$ \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}} \left({x}\right).{ln}\left({sin}\left({x}\right)\right){dx}=? \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 137279 by Ñï= last updated on 31/Mar/21 $$\int\frac{{dx}}{\mathrm{sin}\:\left({a}+{x}\right)\mathrm{cos}\:\left({b}+{x}\right)}=? \\ $$ Answered by Ar Brandon last updated on 31/Mar/21 $$\mathcal{I}=\int\frac{\mathrm{dx}}{\mathrm{sin}\left(\mathrm{a}+\mathrm{x}\right)\mathrm{cos}\left(\mathrm{b}+\mathrm{x}\right)} \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{cos}\left(\mathrm{a}−\mathrm{b}\right)}\int\frac{\mathrm{cos}\left(\mathrm{a}−\mathrm{b}\right)}{\mathrm{sin}\left(\mathrm{a}+\mathrm{x}\right)\mathrm{cos}\left(\mathrm{b}+\mathrm{x}\right)}\mathrm{dx} \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{cos}\left(\mathrm{a}−\mathrm{b}\right)}\int\frac{\mathrm{cos}\left[\left(\mathrm{x}+\mathrm{a}\right)−\left(\mathrm{x}+\mathrm{b}\right)\right]}{\mathrm{sin}\left(\mathrm{a}+\mathrm{x}\right)\mathrm{cos}\left(\mathrm{b}+\mathrm{x}\right)}\mathrm{dx}…
Question Number 71740 by peter frank last updated on 19/Oct/19 $${Derive}\:{the}\:{expression} \\ $$$${for}\:{the}\:{pressure}\:{exerted} \\ $$$${by}\:{an}\:{ideal}\:{gas}\:{on}\:{the} \\ $$$${wall}\:{of}\:{container} \\ $$ Commented by ajfour last updated on…
Question Number 6205 by sanusihammed last updated on 18/Jun/16 $${Show}\:{that} \\ $$$$\int_{\mathrm{42}} ^{\mathrm{7}} \:\left(\mathrm{4}{x}\:−\:\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:{dx}\:\:=\:\:\mathrm{15} \\ $$ Answered by FilupSmith last updated on 18/Jun/16 $$\int_{\mathrm{42}}…
Question Number 6204 by sanusihammed last updated on 18/Jun/16 $${Evaluate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}\left(\sqrt{\mathrm{3}{x}\:−\:\mathrm{4}}\right)\:{dx} \\ $$ Answered by FilupSmith last updated on 18/Jun/16 $${u}=\mathrm{3}{x}−\mathrm{4}\:\Rightarrow\:{du}=\mathrm{3}{dx}\:\rightarrow\:{dx}=\frac{\mathrm{1}}{\mathrm{3}}{du} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{3}}\left({u}+\mathrm{4}\right) \\…