Category: Integration

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 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 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 51910 by Meritguide1234 last updated on 01/Jan/19 Commented by Abdo msup. last updated on 01/Jan/19 $${let}\:{find}\:{firstI}_{{n}} =\:\int_{\mathrm{0}} ^{\pi} \:{cos}^{{n}} {x}\:{cos}\left({nx}\right){dx}\:{with}\:{n}\:{from}\:{N} \\ $$$${I}_{{n}} ={Re}\left(\:\int_{\mathrm{0}}…

Question Number 182962 by universe last updated on 17/Dec/22 Answered by mr W last updated on 17/Dec/22 Commented by mr W last updated on 17/Dec/22…