Question Number 108954 by mnjuly1970 last updated on 20/Aug/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathscr{E}{valuate}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}−{x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} }\:{dxdy}=???\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\bigstar\bigstar\clubsuit\clubsuit\bigstar\bigstar \\ $$$$ \\ $$ Commented…
Question Number 43418 by Raj Singh last updated on 10/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18 $$\int\frac{{cosxdx}}{{sinxcosx}+\mathrm{1}} \\ $$$$\int\frac{\mathrm{2}{cosx}}{\mathrm{2}{cosxsinx}+\mathrm{2}}{dx} \\ $$$$\int\frac{{cosx}+{sinx}+{cosx}−{sinx}}{\mathrm{1}+\left({sinx}+{cosx}\right)^{\mathrm{2}} }{dx} \\ $$$$\int\frac{{cosx}−{sinx}}{\mathrm{1}+\left({sinx}+{cosx}\right)^{\mathrm{2}}…
Question Number 43419 by Raj Singh last updated on 10/Sep/18 Commented by maxmathsup by imad last updated on 10/Sep/18 $${let}\:{A}\:=\:\int\:\:\frac{{xdx}}{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$${A}\:=\:\int\:\:\frac{{x}−\mathrm{1}+\mathrm{1}}{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 43417 by Raj Singh last updated on 10/Sep/18 Commented by alex041103 last updated on 10/Sep/18 $${is}\:{that}\:\sqrt[{{x}}]{{x}^{{n}} +{a}^{{n}} } \\ $$ Commented by maxmathsup…
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Question Number 43386 by ajfour last updated on 10/Sep/18 Commented by ajfour last updated on 10/Sep/18 $${If}\:{the}\:{two}\:{differently}\:{shaded} \\ $$$${areas}\:{are}\:{equal},\:{find}\:{slope}\:\boldsymbol{{m}}\:{of} \\ $$$${line},\:{in}\:{terms}\:{of}\:\boldsymbol{{a}}. \\ $$ Commented by…
Question Number 108921 by Ar Brandon last updated on 20/Aug/20 $$\mathrm{a}.\:\:\int\frac{\mathrm{sin}^{\mathrm{3}} \mathrm{4x}}{\mathrm{cos}^{\mathrm{8}} \mathrm{4x}}\mathrm{dx} \\ $$$$\mathrm{b}.\:\:\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \left(\mathrm{x}^{\mathrm{2}} \mathrm{e}^{\mathrm{cosx}} −\mathrm{2x}\right)\mathrm{sinxdx} \\ $$ Answered by bobhans last…
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Question Number 108893 by bobhans last updated on 20/Aug/20 $$\left(\mathrm{1}\right)\int\:\frac{{x}^{\mathrm{4}} }{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx}\: \\ $$$$\left(\mathrm{2}\right)\underset{−\mathrm{3}} {\overset{\mathrm{5}} {\int}}\sqrt{\mid{x}\mid^{\mathrm{3}} }\:{dx}\: \\ $$$$\left(\mathrm{3}\right)\:\underset{\mathrm{0}} {\overset{\frac{\pi^{\mathrm{2}} }{\mathrm{4}}} {\int}}\:\mathrm{sin}\:\sqrt{{x}}\:{dx}\: \\ $$$$\left(\mathrm{4}\right)\:\underset{−\infty} {\overset{\infty}…