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Category: Integration

Question-43589

Question Number 43589 by Tawa1 last updated on 12/Sep/18 Commented by maxmathsup by imad last updated on 12/Sep/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\beta}{\mathrm{10}\:+\mathrm{8}{sin}\beta}\:{d}\beta\:\:\:{changement}\:\:{e}^{{i}\beta} ={z}\:{give} \\ $$$${I}\:\:=\:\int_{\mid{z}\mid=\mathrm{1}} \:\:\:\:\:\frac{\frac{{z}+{z}^{−\mathrm{1}}…

Given-a-function-f-x-3-f-x-for-x-R-If-3-6-f-x-dx-6-then-3-9-f-x-dx-

Question Number 109101 by bemath last updated on 21/Aug/20 $$\:{Given}\:{a}\:{function}\:{f}\left({x}+\mathrm{3}\right)={f}\left({x}\right) \\ $$$${for}\:\forall{x}\in\mathbb{R}.\:{If}\:\underset{−\mathrm{3}} {\overset{\mathrm{6}} {\int}}{f}\left({x}\right){dx}\:=\:−\mathrm{6}\: \\ $$$${then}\:\underset{\mathrm{3}} {\overset{\mathrm{9}} {\int}}{f}\left({x}\right)\:{dx}\:=\:? \\ $$ Answered by bemath last updated…

x-1-csc-x-dx-

Question Number 174628 by cortano1 last updated on 06/Aug/22 $$\:\:\:\Omega\:=\:\int\:\frac{{x}}{\mathrm{1}+\mathrm{csc}\:{x}}\:{dx}\:=? \\ $$ Commented by infinityaction last updated on 06/Aug/22 $$\int\frac{{x}}{\mathrm{1}+\mathrm{csc}{x}}{dx}=\int\frac{{xs}\mathrm{in}{x}}{\mathrm{1}+\mathrm{sin}{x}}{dx} \\ $$$$=\int{x}\frac{\mathrm{1}+\mathrm{sin}{x}−\mathrm{1}}{\mathrm{1}+\mathrm{sin}{x}}{dx}=\int\left({x}−\frac{{x}}{\mathrm{1}+\mathrm{sin}{x}}\right){dx} \\ $$$$\Omega\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}−\int\frac{{x}}{\underset{{I}}…

o-h-ans-1-x-2-e-y-x-y-2-dx-xy-dy-2-f-x-x-x-2-e-x-2-f-1-1-e-g-x-4-e-4-1-x-e-t-2-f-t-dt-find-f-2-g-2-

Question Number 109086 by bobhans last updated on 21/Aug/20 $$\:\:\:\underset{\rightarrow} {\flat}\underset{\rightarrow} {{o}}\flat\underset{\multimap} {{h}an}\underset{\multimap} {{s}} \\ $$$$\left(\mathrm{1}\right)\:\left({x}^{\mathrm{2}} {e}^{−\frac{{y}}{{x}}} +{y}^{\mathrm{2}} \right)\:{dx}\:=\:{xy}\:{dy}\: \\ $$$$\left(\mathrm{2}\right)\left(\frac{{f}\left({x}\right)}{{x}}\right)'\:=\:{x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } \:;\:{f}\left(\mathrm{1}\right)\:=\:\frac{\mathrm{1}}{{e}}\: \\…

evaluate-1-cos-x-a-cos-x-b-dx-

Question Number 43551 by peter frank last updated on 11/Sep/18 $${evaluate}\:\int\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}−{a}\right)\mathrm{cos}\:\left({x}−{b}\right)}{dx} \\ $$ Answered by MJS last updated on 12/Sep/18 $$\int\frac{{dx}}{\mathrm{cos}\left({x}−{a}\right)\mathrm{cos}\left({x}−{b}\right)}= \\ $$$$\:\:\:\:\:\left[{t}={x}−{a}\:\rightarrow\:{dx}={dt}\right] \\ $$$$=\int\frac{{dt}}{\mathrm{cos}\:{t}\:\mathrm{cos}\left({t}+{a}−{b}\right)}=…

calculate-0-x-1-0-y-1-x-2y-e-2x-y-dxdy-

Question Number 43539 by abdo.msup.com last updated on 11/Sep/18 $${calculate}\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\mathrm{0}\leqslant{y}\leqslant\mathrm{1}} \:\:\left({x}+\mathrm{2}{y}\right){e}^{\mathrm{2}{x}−{y}} {dxdy} \\ $$ Commented by maxmathsup by imad last updated on 16/Sep/18 $${let}\:{consider}\:{the}\:{diffeomorphisme}\:\left({u},{v}\right)\:\rightarrow\varphi\left({u},{v}\right)=\left(\varphi_{\mathrm{1}} \left({u},{v}\right),\varphi_{\mathrm{2}}…