Menu Close

Category: Integration

56546557-vb65-

Question Number 141 by shahid.ansari56@yahoo.com last updated on 25/Jan/15 $$\mathrm{56546557}\boldsymbol{\div}{vb}\mathrm{65} \\ $$$$ \\ $$ Answered by 123456 last updated on 14/Dec/14 $$\frac{\mathrm{56546557}}{\mathrm{65}{vb}},{vb}\neq\mathrm{0} \\ $$ Terms…

calculus-prove-that-0-4-tan-x-tan-2-x-tan-x-tan-2-x-sin-x-dx-1-2-8-1-4-3-4-3-4-5-4-

Question Number 131211 by mnjuly1970 last updated on 02/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…{calculus}… \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\boldsymbol{\Phi}=\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \left(\frac{\sqrt{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)}}{\:\sqrt{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)−\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)}}\:\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)\right)\boldsymbol{{dx}}\: \\ $$$$\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\boldsymbol{\pi}}}{\mathrm{8}}\:\left(\frac{\boldsymbol{\Gamma}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\boldsymbol{\Gamma}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)}−\frac{\boldsymbol{\Gamma}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)}{\boldsymbol{\Gamma}\left(\frac{\mathrm{5}}{\mathrm{4}}\right)}\right) \\ $$ Answered by Ar…

Question-131183

Question Number 131183 by john_santu last updated on 02/Feb/21 Answered by liberty last updated on 02/Feb/21 $$\:\frac{\mathrm{dP}}{\left(\mathrm{32}−\mathrm{P}\right)\mathrm{P}}\:=\:\mathrm{0}.\mathrm{0015}\:\mathrm{dt}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{32}}\:\int\:\left[\:\frac{\mathrm{1}}{\mathrm{32}−\mathrm{P}}\:+\frac{\mathrm{1}}{\mathrm{P}}\:\right]\mathrm{dP}\:=\:\int\mathrm{0}.\mathrm{0015}\:\mathrm{dt} \\ $$$$\frac{\mathrm{1}}{\mathrm{32}}\:\mathrm{ln}\:\mid\frac{\mathrm{P}}{\mathrm{32}−\mathrm{P}}\:\mid\:=\:\mathrm{0}.\mathrm{0015t}\:+\:\mathrm{c}\: \\ $$$$\mathrm{ln}\:\mid\frac{\mathrm{P}}{\mathrm{32}−\mathrm{P}}\mid\:=\:\mathrm{0}.\mathrm{48t}+\mathrm{C}\:;\:\frac{\mathrm{P}\left(\mathrm{t}\right)}{\mathrm{32}−\mathrm{P}\left(\mathrm{t}\right)}\:=\:\lambda\mathrm{e}^{\mathrm{0}.\mathrm{048t}} \\ $$$$\Leftrightarrow\:\frac{\mathrm{32}−\mathrm{P}\left(\mathrm{t}\right)}{\mathrm{P}\left(\mathrm{t}\right)}\:=\:\frac{\mathrm{1}}{\lambda}\mathrm{e}^{−\mathrm{0}.\mathrm{048t}}…

cos-ln-a-x-k-dx-

Question Number 131176 by Raxreedoroid last updated on 02/Feb/21 $$\int\frac{{cos}\left({ln}\left({a}^{{x}} \right)\right)}{\:\sqrt{{k}}}{dx}=?? \\ $$ Answered by Ar Brandon last updated on 02/Feb/21 $$\mathrm{I}=\int\frac{\mathrm{cos}\left(\mathrm{lna}^{\mathrm{x}} \right)}{\:\sqrt{\mathrm{k}}}\mathrm{dx}\:,\:\mathrm{t}=\mathrm{lna}^{\mathrm{x}} \:\Rightarrow\mathrm{dt}=\mathrm{lnadx} \\…