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Category: Integration

Question-91217

Question Number 91217 by mhmd last updated on 28/Apr/20 Commented by Prithwish Sen 1 last updated on 28/Apr/20 $$\int_{\mathrm{0}} ^{\mathrm{n}\pi} \mid\mathrm{cosx}\mid\mathrm{dx}\:=\:\boldsymbol{\mathrm{n}}\int_{\mathrm{0}} ^{\boldsymbol{\pi}} \mid\mathrm{cosx}\mid\mathrm{dx}\:=\:\mathrm{n}\left[\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{\mathrm{cosxdx}}+\int_{\frac{\boldsymbol{\pi}}{\mathrm{2}}}…

Question-156743

Question Number 156743 by cortano last updated on 15/Oct/21 Answered by MJS_new last updated on 15/Oct/21 $$\mathrm{0}\leqslant{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow \\ $$$$\int\frac{{dx}}{\:\sqrt[{\mathrm{4}}]{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} \left(\mathrm{1}−{x}\right)^{\mathrm{6}} }}= \\ $$$$=\int\frac{{dx}}{\:\left(\mathrm{1}−{x}\right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}= \\…

Question-156739

Question Number 156739 by cortano last updated on 15/Oct/21 Commented by john_santu last updated on 15/Oct/21 $$\:{B}=\int\:\sqrt{\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}}\:{dx} \\ $$$$\:\:\:=\int\:\sqrt{\frac{\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)}{−\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)}}\:{dx} \\ $$$$\:\:=\int\:\sqrt{−\mathrm{tan}\:\:\left({x}+\frac{\pi}{\mathrm{4}}\right)}\:{dx} \\ $$$$\:\:=\int\sqrt{\mathrm{cot}\:\left({x}+\frac{\mathrm{3}\pi}{\mathrm{4}}\right)}\:{d}\left({x}+\frac{\mathrm{3}\pi}{\mathrm{4}}\right) \\ $$$$\:=\int\:\frac{{dq}}{\:\sqrt{\mathrm{tan}\:{q}}}\:…

sin-ln-x-dx-

Question Number 156695 by amin96 last updated on 14/Oct/21 $$\int{sin}\left({ln}\left({x}\right)\right){dx}=? \\ $$ Answered by puissant last updated on 10/Nov/21 $${Q}=\int_{\mathrm{0}} ^{\mathrm{1}} {sin}\left({lnx}\right){dx}\:;\:{u}={lnx}\rightarrow{x}={e}^{{u}} \rightarrow{dx}={e}^{{u}} {du} \\…