Question Number 38720 by maxmathsup by imad last updated on 28/Jun/18 $${find}\:\:\:\int\:\:\:\:\:\frac{\sqrt{{x}+\mathrm{1}}\:−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}\:−\sqrt{{x}−\mathrm{1}}}{dx} \\ $$ Commented by math khazana by abdo last updated on 28/Jun/18 $${the}\:{Q}\:{is}\:{find}\:\:\int\:\:\:\:\frac{\sqrt{{x}+\mathrm{1}}\:−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}−\mathrm{1}}}{dx}…
Question Number 38718 by maxmathsup by imad last updated on 28/Jun/18 $$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{2}+{x}\:{cos}\theta\right){d}\theta \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{2}\:\:+{cos}\theta\right){d}\theta \\ $$$$ \\ $$ Commented by math…
Question Number 38716 by maxmathsup by imad last updated on 28/Jun/18 $${calculate}\:\:\:\int_{\mathrm{2}} ^{\mathrm{5}} \:\:\:\:\:\frac{{dx}}{\left({x}\:+\mathrm{1}−\left[{x}\right]\right)^{\mathrm{2}} } \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 38714 by maxmathsup by imad last updated on 28/Jun/18 $${calculate}\:\:\:\int_{\mathrm{1}} ^{\mathrm{6}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{1}+{x}^{\mathrm{2}} \left[{x}\right]}{dx} \\ $$ Commented by abdo mathsup 649 cc last…
Question Number 38706 by abdo mathsup 649 cc last updated on 28/Jun/18 $${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{d}\theta}{\mathrm{1}+{x}\:{e}^{{i}\theta} }\:\:\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{e}^{{i}\theta} }{\left(\mathrm{1}+{x}\:{e}^{{i}\theta}…
Question Number 104220 by bemath last updated on 20/Jul/20 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{x}^{\mathrm{2}} \mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\:{dx}\:?\: \\ $$ Commented by bemath last updated on 20/Jul/20 $${thank}\:{you}\:{both}.\:{cooll} \\…
Question Number 104197 by mathmax by abdo last updated on 20/Jul/20 $$\mathrm{calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{9}\right)^{\mathrm{4}} } \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 38651 by rahul 19 last updated on 28/Jun/18 $$\mathrm{If}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{e}^{−{x}^{\mathrm{2}} } {dx}\:=\:{a}\:,\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } {dx}\:{in}\:{terms}\:{of}\:'{a}'\:? \\ $$ Answered…
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Question Number 169706 by MikeH last updated on 06/May/22 $$\mathrm{using}\:\mathrm{cylindrical}\:\mathrm{coordinates}\:\begin{cases}{{x}={r}\mathrm{cos}\theta}\\{{y}\:=\:{r}\mathrm{sin}\:\theta}\\{{z}={z}}\end{cases} \\ $$$$\mathrm{to}\:\mathrm{evaluate}\:\mathrm{the}\:\mathrm{integral} \\ $$$${K}=\:\int\int\int_{{S}} \sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{z}^{\mathrm{2}} }\:{dxdydz} \\ $$$$\mathrm{where} \\ $$$$\:{S}=\:\left\{\left({x},{y},{z}\right)\:\in\mathbb{R}^{\mathrm{3}} :\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:\leqslant\:\mathrm{4},\:\mathrm{0}\:\leqslant{z}\leqslant\sqrt{{x}^{\mathrm{2}}…