Question Number 51988 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{f}\left({a}\right)\:=\int\:\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{4}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int\:\:\:\:\frac{{dx}}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{4}} }} \\ $$$${a}>\mathrm{0} \\ $$ Terms…
Question Number 51989 by maxmathsup by imad last updated on 01/Jan/19 $${calculate}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\frac{{sinx}}{\mathrm{1}+{sin}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by peter frank last updated on 01/Jan/19…
Question Number 51987 by maxmathsup by imad last updated on 01/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$ Commented by Abdo msup. last updated on 02/Jan/19…
Question Number 117511 by Canovas last updated on 12/Oct/20 Answered by bemath last updated on 12/Oct/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\left(\mathrm{4}−\mathrm{9tan}\:^{\mathrm{2}} \mathrm{x}\right)}\:=\:\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{4}−\mathrm{9tan}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx} \\ $$$$=\:\int\:\frac{\mathrm{d}\left(\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{4}−\mathrm{9tan}\:^{\mathrm{2}} \mathrm{x}}\:=\:\int\:\frac{\mathrm{d}\varphi}{\mathrm{4}−\mathrm{9}\varphi^{\mathrm{2}} }…
Question Number 117496 by bemath last updated on 12/Oct/20 $$\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \theta\:\mathrm{tan}\:^{\mathrm{2}} \theta}{\:\sqrt{\mathrm{9}−\mathrm{tan}\:^{\mathrm{2}} \theta}}\:\mathrm{d}\theta\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 12/Oct/20 $$\int\frac{{t}^{\mathrm{2}} {dt}}{\:\sqrt{\mathrm{9}−{t}^{\mathrm{2}}…
Question Number 51959 by ajfour last updated on 01/Jan/19 Commented by ajfour last updated on 01/Jan/19 $${Find}\:{the}\:{length}\:{of}\:{one}\:{turn} \\ $$$${uniform}\:\frac{{dz}}{{d}\theta}\:\:{helix}\:{around}\:{the} \\ $$$${cylinder}. \\ $$ Commented by…
Question Number 183031 by universe last updated on 18/Dec/22 Answered by aleks041103 last updated on 23/Dec/22 $$\left({x},{y}\right)\in{T}\left({G}\right) \\ $$$$\Rightarrow\frac{\pi}{\mathrm{2}}{s}\left(\mathrm{1}−{t}\right)={x} \\ $$$$\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−{s}\right)={y}\Rightarrow{s}=\mathrm{1}−\frac{\mathrm{2}{y}}{\pi}\Rightarrow{x}=\left(\frac{\pi}{\mathrm{2}}−{y}\right)\left(\mathrm{1}−{t}\right) \\ $$$$\mathrm{0}<{s}<\mathrm{1}\Rightarrow\mathrm{0}<{y}<\pi/\mathrm{2} \\ $$$$\Rightarrow\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}}−{y}…
Question Number 117463 by mnjuly1970 last updated on 11/Oct/20 Commented by mindispower last updated on 11/Oct/20 $${nice}\:{sir} \\ $$ Commented by mnjuly1970 last updated on…
Question Number 182995 by universe last updated on 18/Dec/22 Answered by som(math1967) last updated on 18/Dec/22 Commented by som(math1967) last updated on 18/Dec/22 $$\:{Area}=\mathrm{4}×\left\{\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 117446 by Ar Brandon last updated on 11/Oct/20 $$\mathrm{Evaluate}\:\int\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}}{{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{25}}\mathrm{d}{x} \\ $$ Answered by Ar Brandon last updated on 11/Oct/20 $$\mathcal{I}=\int\frac{\mathrm{3}{x}^{\mathrm{2}}…