Question Number 161212 by cortano last updated on 14/Dec/21 $$\:\:\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{x}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}{\mathrm{cos}\:^{\mathrm{4}} {x}\:+\mathrm{sin}\:^{\mathrm{4}} {x}}\:{dx}\:=? \\ $$ Commented by puissant last updated on 15/Dec/21 Commented by…
Question Number 95691 by mathmax by abdo last updated on 27/May/20 $$\mathrm{calculate}\:\int\:\:\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt{\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{2}−\mathrm{x}\right)}}\mathrm{dx} \\ $$ Commented by Tony Lin last updated on 27/May/20 $$\int\frac{{x}+\mathrm{1}}{\:\sqrt{\left({x}+\mathrm{3}\right)\left(\mathrm{2}−{x}\right)}}{dx} \\ $$$$=\int\frac{{x}+\mathrm{1}}{\:\sqrt{−{x}^{\mathrm{2}}…
Question Number 95673 by Rio Michael last updated on 26/May/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{3}\:+\:\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} }\:}\:{dx}\:=\:? \\ $$ Commented by Tony Lin last updated on 26/May/20 $$\int_{\mathrm{0}}…
Question Number 95653 by rb222 last updated on 26/May/20 $${arc}\:{length}\:\mathrm{3}{x}^{\frac{\mathrm{3}}{\mathrm{2}}} −\mathrm{1}\: \\ $$$${from}\:{x}=\mathrm{0}\:{and}\:{x}=\mathrm{1}\: \\ $$$${help}\:{please}\:{sir} \\ $$ Answered by john santu last updated on 26/May/20…
Question Number 95650 by M±th+et+s last updated on 26/May/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left\{\left(−\mathrm{1}\right)^{\lfloor\frac{\mathrm{1}}{{x}}\rfloor} \frac{\mathrm{1}}{{x}}\right\}{dx} \\ $$$$\left\{..\right\}{is}\:{fractional}\:{part} \\ $$$$\lfloor..\rfloor\:{is}\:{floor}\:{function} \\ $$ Answered by mathmax by abdo last…
Question Number 161176 by mnjuly1970 last updated on 13/Dec/21 $$ \\ $$$$\:\:\:\:\:\:{calculate}\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\Theta\::=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\:\right)^{\:{n}−\mathrm{1}} }{{n}\:\left(\:{n}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\:\right)}\:=?\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:\:{m}.{n} \\ $$$$\:\:\:\:\:\:\:−−−−−−−−−−−−− \\ $$$$ \\ $$…
Question Number 161178 by amin96 last updated on 13/Dec/21 $$\underset{\mathrm{2}} {\int}^{\infty} \frac{\boldsymbol{{arctg}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{arctg}}\left(\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)}\boldsymbol{{dx}}=??? \\ $$ Answered by MJS_new last updated on 13/Dec/21 $$\mathrm{1}<\frac{\mathrm{arctan}\:{x}}{\mathrm{arctan}\:\frac{{x}}{\mathrm{2}}}\leqslant\mathrm{2} \\ $$$$\Rightarrow \\…
Question Number 95624 by i jagooll last updated on 26/May/20 $$\overset{\mathrm{5}} {\int}_{\mathrm{1}} {x}\left(\int\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right)\:{dx}\:=\:\mathrm{24} \\ $$$$\overset{\mathrm{3}} {\int}_{\mathrm{1}} \left(\mathrm{2}−\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}\:?\: \\ $$ Answered by Racoon last updated on…
Question Number 95592 by i jagooll last updated on 26/May/20 $$\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}\:+\:\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}\:\mathrm{dx} \\ $$ Commented by PRITHWISH SEN 2 last updated on 26/May/20 $$\int\frac{\mathrm{2sin}\:\mathrm{2x}\:\mathrm{dx}}{\mathrm{2}−\mathrm{sin}\:^{\mathrm{2}}…
Question Number 95593 by Rio Michael last updated on 26/May/20 $$\mathrm{if}\:{f}\left({x}\right)\:=\:\frac{\mathrm{sin}\:{x}}{\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \:+{x}^{\mathrm{6}} \right)^{\mathrm{2}} }\:\mathrm{is}\:\mathrm{odd}, \\ $$$$\mathrm{find}\:\underset{−\mathrm{3}} {\overset{\mathrm{3}} {\int}}{f}\left({x}\right)\:{dx} \\ $$ Commented by PRITHWISH SEN 2…