Question Number 64328 by Chi Mes Try last updated on 16/Jul/19 $$\mathrm{Let}\:\:{f}\::\:{R}\rightarrow{R},\:{g}\::\:{R}\rightarrow{R}\:\:\mathrm{be}\:\mathrm{continuous} \\ $$$$\mathrm{functions}.\:\mathrm{Then} \\ $$$$\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\:\left[\:{f}\left({x}\right)+{f}\left(−{x}\right)\:\right]\:\left[\:{g}\left({x}\right)\left({g}\left(−{x}\right)\:\right]\:{dx}\:=\right. \\ $$ Terms of Service Privacy Policy…
Question Number 64327 by Chi Mes Try last updated on 16/Jul/19 $$\frac{{d}}{{dx}}\:\:\left(\:\underset{{f}\left({x}\right)} {\overset{{g}\left({x}\right)} {\int}}\:\phi\left({t}\right)\:{dt}\:\right)\:= \\ $$ Commented by mathmax by abdo last updated on 16/Jul/19…
Question Number 64269 by Chi Mes Try last updated on 16/Jul/19 $$\underset{−\pi} {\overset{\pi} {\int}}\:\left[\mathrm{cos}\:{px}−\mathrm{sin}\:{qx}\right]^{\mathrm{2}} {dx},\:\mathrm{where}\:{p},\:{q}\:\mathrm{are}\: \\ $$$$\mathrm{integers}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by Tanmay chaudhury last updated…
Question Number 64268 by Chi Mes Try last updated on 16/Jul/19 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}^{\mathrm{99}} +\mathrm{2}^{\mathrm{99}} +…+\:{n}^{\mathrm{99}} }{{n}^{\mathrm{100}} }\:= \\ $$ Commented by Prithwish sen last updated…
Question Number 64266 by Chi Mes Try last updated on 16/Jul/19 $$\:\underset{\mathrm{1}/{e}} {\overset{{e}} {\int}}\:\mid\:\mathrm{log}\:{x}\:\mid\:{dx}\:= \\ $$ Answered by ajfour last updated on 16/Jul/19 $${I}=−\int_{\mathrm{1}/{e}} ^{\:\:\mathrm{1}}…
Question Number 64267 by Chi Mes Try last updated on 16/Jul/19 $$\mathrm{If}\:\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:\:\frac{\mathrm{1}}{{a}+{b}\:\mathrm{cos}\:{x}}\:{dx},\:{a}>\mathrm{0}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\frac{\pi}{\:\sqrt{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }}\:, \\ $$$$\mathrm{then}\:\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:\:\:\frac{\mathrm{1}}{\left({a}+{b}\:\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx}\:= \\ $$ Commented by…
Question Number 64265 by Chi Mes Try last updated on 16/Jul/19 $$\mathrm{If}\:\underset{\mathrm{log}\:\mathrm{2}} {\overset{{x}} {\int}}\:\:\frac{\mathrm{1}}{\:\sqrt{{e}^{{x}} −\mathrm{1}}}\:{dx}\:=\:\frac{\pi}{\mathrm{6}},\:\mathrm{then}\:{x}\:= \\ $$ Commented by mathmax by abdo last updated on…
Question Number 64225 by mmkkmm000m last updated on 16/Jul/19 $$\mathrm{Solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\underset{\:\sqrt{\mathrm{2}}} {\overset{{x}} {\int}}\:\:\:\frac{{dx}}{{x}\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:=\:\frac{\pi}{\mathrm{12}}\:\:\mathrm{is}\:\:{x}\:=\:\_\_\_\_\_. \\ $$ Answered by ajfour last updated on 16/Jul/19 $$\mathrm{cos}^{−\mathrm{1}}…
Question Number 64139 by Chi Mes Try last updated on 14/Jul/19 $$\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}\:\mathrm{cos}\:\alpha+\mathrm{1}}\:=\:\alpha\:\mathrm{sin}\:\alpha \\ $$ Commented by Prithwish sen last updated on 14/Jul/19…
Question Number 64080 by Chi Mes Try last updated on 12/Jul/19 $$\int\frac{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}}\:{e}^{\mathrm{sin}\:{x}} \mathrm{cos}\:{x}\:{dx}\:= \\ $$ Commented by som(math1967) last updated on 13/Jul/19 $${e}^{{sinx}} +{c} \\…