Question Number 27595 by abdo imad last updated on 10/Jan/18 $${find}\:\:\int\int_{{D}} \:\:{xy}\sqrt{\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:{dxdy}\:\:\:{with} \\ $$$${D}=\left\{\:\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\:\:,{x}\geqslant\mathrm{0}\:,{y}\:\geqslant\mathrm{0}\right\} \\ $$ Commented by abdo imad…
Question Number 27596 by abdo imad last updated on 10/Jan/18 $${find}\:\:\int\:\:\:^{\mathrm{3}} \sqrt{\:{x}^{\mathrm{2}} −{x}^{\mathrm{3}} }\:\:{dx} \\ $$ Commented by abdo imad last updated on 28/Jan/18 $${I}=\:\int\:\:\:\:^{\mathrm{3}}…
Question Number 93109 by Mikael_786 last updated on 10/May/20 $$\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\:{cos}^{\mathrm{2020}} \left({x}\right){dx} \\ $$ Commented by prakash jain last updated on 11/May/20 $$\int_{\mathrm{9}} ^{\mathrm{2}\pi}…
Question Number 93098 by Rio Michael last updated on 10/May/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to} \\ $$$$\:\int\:\frac{\mathrm{1}}{{a}\:\mathrm{sin}\:{x}\:+\:{b}\:\mathrm{cos}\:{x}}\:{dx}\:\:\mathrm{and}\:\int\:\frac{\mathrm{1}}{{a}\:\mathrm{cos}\:{x}\:−\:{b}\mathrm{sin}\:{x}}\:{dx} \\ $$$$\mathrm{where}\:{a}\:,\:{b}\:\mathrm{are}\:\mathrm{constants}. \\ $$$$ \\ $$ Commented by prakash jain last updated…
Question Number 27539 by Mr eaay last updated on 08/Jan/18 Commented by Tinkutara last updated on 08/Jan/18 For second part see question 27445 and 27400. Answered by Joel578 last updated on 09/Jan/18…
Question Number 158596 by mnjuly1970 last updated on 06/Nov/21 $$ \\ $$$$\:\:\:\:\:{calculate}\:: \\ $$$$\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\:\mathrm{1}+\:{tan}^{\:\mathrm{4}} \left({x}\right)}{{cot}^{\:\mathrm{2}} \left({x}\right)}\:{dx}=? \\ $$$$ \\ $$ Answered by puissant…
Question Number 93061 by Ar Brandon last updated on 10/May/20 $$\int_{\mathrm{1}} ^{+\infty} \frac{\mathrm{sin}\:\mathrm{u}}{\mathrm{u}}\mathrm{du} \\ $$ Commented by mathmax by abdo last updated on 10/May/20 $${we}\:{have}\frac{\pi}{\mathrm{2}}\:=\int_{\mathrm{0}}…
Question Number 158591 by cortano last updated on 06/Nov/21 $$\:{I}=\int\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{6}} }\:=? \\ $$ Commented by tounghoungko last updated on 06/Nov/21 $${I}=\int\:\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}\:{dx}−\int\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{6}} +\mathrm{1}}\:{dx}…
Question Number 158590 by mnjuly1970 last updated on 06/Nov/21 $$ \\ $$$$\:\:\:{prove}\:{that}\: \\ $$$$\mathrm{1}.\:\mathrm{I}=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{sin}\left(\:{x}+{tan}\left({x}\right)\right)}{{sin}\left({x}\right)}{dx}\:=\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{2}.\:\mathrm{J}\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{sin}\left({x}−{tan}\left({x}\right)\right)}{{sin}\left({x}\right)}{dx}=\left(\frac{\mathrm{1}}{{e}}\:−\frac{\mathrm{1}}{\mathrm{2}}\right)\pi \\ $$$$ \\ $$ Answered…
Question Number 93045 by john santu last updated on 10/May/20 $$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\frac{{x}}{\mathrm{2}}}\right)\:{dx}\: \\ $$ Commented by mathmax by abdo last updated on 10/May/20 $${I}\:=\int\:\:{arcsin}\left(\sqrt{\frac{{x}}{\mathrm{2}}}\right){dx}\:\:\:\:{changement}\:\sqrt{\frac{{x}}{\mathrm{2}}}={t}\:{give}\:\frac{{x}}{\mathrm{2}}={t}^{\mathrm{2}} \:\Rightarrow{x}=\mathrm{2}{t}^{\mathrm{2}}…