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Category: Integration

If-1-4-f-x-dx-5-what-is-the-value-of-0-1-f-3x-1-dx-

Question Number 22166 by Joel577 last updated on 12/Oct/17 $$\mathrm{If}\underset{\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\mathrm{5} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{f}\left(\mathrm{3}{x}\:+\mathrm{1}\right)\:{dx}\:? \\ $$ Answered by ajfour last updated on 12/Oct/17…

integrate-cosx-cos2x-1-cosx-dx-

Question Number 22151 by j.masanja06@gmail.com last updated on 12/Oct/17 $${integrate} \\ $$$$\int\frac{{cosx}−{cos}\mathrm{2}{x}}{\mathrm{1}+{cosx}}{dx} \\ $$ Answered by $@ty@m last updated on 12/Oct/17 $$=\int\frac{{cosx}−\left(\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}\right)}{\mathrm{1}+{cosx}}{dx} \\ $$$$=\int\frac{\mathrm{1}+\mathrm{cos}{x}\:−\mathrm{2cos}\:^{\mathrm{2}}…

ln-x-1-x-2-1-x-2-dx-

Question Number 87686 by M±th+et£s last updated on 05/Apr/20 $$\int\sqrt{\frac{{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 05/Apr/20 $${t}^{\mathrm{2}} ={ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\right)…

Question-87585

Question Number 87585 by Power last updated on 05/Apr/20 Answered by redmiiuser last updated on 05/Apr/20 $${arc}\mathrm{sin}\:{x}+\mathrm{arccos}\:{x}=\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{arcsin}\:{x}.\mathrm{arccos}\:{x}=\frac{\pi}{\mathrm{2}}\mathrm{arcsin}\:{x}−\left(\mathrm{arcsin}\:{x}\right)^{\mathrm{2}} \\ $$$$\mathrm{arcsin}\:{x}={t} \\ $$$${dx}=\mathrm{cos}\:{t}.{dt} \\ $$$${x}=\mathrm{sin}\:{t}…