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Category: Integration

given-f-x-f-x-pi-6-x-R-if-0-pi-6-f-x-dx-T-then-pi-7pi-3-f-x-pi-dx-

Question Number 82223 by jagoll last updated on 19/Feb/20 $${given}\:{f}\left({x}\right)\:=\:{f}\left({x}+\frac{\pi}{\mathrm{6}}\right)\:,\:\forall{x}\in\:\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{6}}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:{T}\: \\ $$$${then}\:\underset{\pi} {\overset{\frac{\mathrm{7}\pi}{\mathrm{3}}} {\int}}\:{f}\left({x}+\pi\right)\:{dx}\:=\:? \\ $$ Commented by john santu last…

2-x-2-2-x-2-4-x-4-dx-

Question Number 147749 by cesarL last updated on 23/Jul/21 $$\int\frac{\sqrt{\mathrm{2}−{x}^{\mathrm{2}} }+\sqrt{\mathrm{2}+{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{4}−{x}^{\mathrm{4}} }}{dx} \\ $$ Answered by mathmax by abdo last updated on 23/Jul/21 $$\mathrm{I}=\int\:\frac{\sqrt{\mathrm{2}−\mathrm{x}^{\mathrm{2}}…

Question-147746

Question Number 147746 by 0731619 last updated on 23/Jul/21 Answered by mindispower last updated on 23/Jul/21 $$\frac{{tan}^{−} \left({x}^{\mathrm{2}} \right)}{{tan}^{−} \left({x}\right)}<\mathrm{1} \\ $$$${x}\leqslant{x}^{\mathrm{2}} <\mathrm{1},\:{and}\:{using}\:{tan}^{−} \:{increasing}\:{function} \\…

dx-sec-x-csc-x-

Question Number 82185 by jagoll last updated on 19/Feb/20 $$\int\:\frac{{dx}}{\mathrm{sec}\:{x}\:+\:{csc}\:{x}}\:=\:?\: \\ $$ Commented by john santu last updated on 19/Feb/20 $$\mathrm{sec}\:{x}+\:{csc}\:{x}\:=\:\frac{\mathrm{1}}{\mathrm{cos}\:{x}}+\frac{\mathrm{1}}{\mathrm{sin}\:{x}} \\ $$$$\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}\:. \\ $$$$\int\:\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}\:{dx}\:=\:…

let-F-x-1-x-1-5-2x-3-4-1-find-F-x-dx-2-en-deduire-la-decomposition-de-F-en-element-simples-

Question Number 147683 by mathmax by abdo last updated on 22/Jul/21 $$\mathrm{let}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{5}} \left(\mathrm{2x}−\mathrm{3}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\int\:\mathrm{F}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\mathrm{en}\:\mathrm{deduire}\:\mathrm{la}\:\mathrm{decomposition}\:\mathrm{de}\:\mathrm{F}\:\mathrm{en}\:\mathrm{element}\:\mathrm{simples} \\ $$ Answered by mathmax by abdo…