Question Number 53295 by gunawan last updated on 20/Jan/19 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{\mathrm{2}+\mathrm{cos}\:{x}}\:{dx}=… \\ $$ Commented by maxmathsup by imad last updated on 20/Jan/19 $${changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give}\: \\…
Question Number 53293 by gunawan last updated on 20/Jan/19 $$\int_{−\mathrm{1}/\mathrm{2}} ^{\mathrm{1}/\mathrm{2}} \mid{x}\mathrm{cos}\:\frac{\pi{x}}{\mathrm{2}}\mid\:{dx}=… \\ $$ Commented by maxmathsup by imad last updated on 20/Jan/19 $${we}\:{have}\:{f}\left({x}\right)=\mid{xcos}\left(\frac{\pi{x}}{\mathrm{2}}\right)\mid=\mid{x}\mid\mid{cos}\left(\frac{\pi{x}}{\mathrm{2}}\right)\mid\:{is}\:{a}\:{even}\:{function}\:{so} \\…
Question Number 53294 by gunawan last updated on 20/Jan/19 $$\int_{−\mathrm{1}/\mathrm{2}} ^{\mathrm{1}/\mathrm{2}} \left[\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)^{\mathrm{2}} −\mathrm{2}\right]^{\mathrm{1}/\mathrm{2}} {dx}=… \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 20/Jan/19 $${f}\left({x}\right)=\left[\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)^{\mathrm{2}}…
Question Number 53292 by gunawan last updated on 20/Jan/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{{x}^{\mathrm{2}} } {dx}=.. \\ $$ Commented by maxmathsup by imad last updated on 20/Jan/19…
Question Number 53284 by maxmathsup by imad last updated on 20/Jan/19 $${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({xt}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:\:\:{with}\:{x}\:{real}\:. \\ $$ Commented by prof Abdo imad last updated on…
Question Number 53285 by maxmathsup by imad last updated on 20/Jan/19 $${let}\:{I}_{\lambda} \:=\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{xdx}}{{cos}^{\mathrm{2}} {x}\:+\lambda^{\mathrm{2}} {sin}^{\mathrm{2}} {x}}\:\:{with}\:\lambda\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:{I}_{\lambda} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{xdx}}{{a}^{\mathrm{2}} {cos}^{\mathrm{2}}…
Question Number 118819 by bramlexs22 last updated on 20/Oct/20 $$\int\frac{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{4}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:{dx}\: \\ $$ Answered by MJS_new last updated on 20/Oct/20 $$=\int\frac{\mathrm{13}\left({x}^{\mathrm{2}}…
Question Number 53271 by Abdo msup. last updated on 19/Jan/19 $$\left.\mathrm{1}\right){calculate}\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−{xt}^{\mathrm{2}} } {dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{t}^{\mathrm{2}} } \:−{e}^{−\mathrm{2}{t}^{\mathrm{2}} } }{{t}^{\mathrm{2}} }\:{dt}\:\:{by}\:{using} \\…
Question Number 53270 by Abdo msup. last updated on 19/Jan/19 $$\left.\mathrm{1}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{at}} {dt}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){by}\:{using}\:{fubinni}\:{theorem}\:{find}\:{the}\:{value}\:{of} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{t}} \:−{e}^{−{xt}} }{{t}}{dt}\:\:\:{with}\:{x}>\mathrm{0}\:. \\ $$ Commented…
Question Number 53261 by Abdo msup. last updated on 19/Jan/19 $$\left.\mathrm{1}\right){find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−\mathrm{2}{t}} {ln}\left(\mathrm{1}−{xt}\right){dt}\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−\mathrm{2}{t}} {ln}\left(\mathrm{1}−\frac{{t}\sqrt{\mathrm{2}}}{\mathrm{2}}\right){dt}. \\ $$ Terms of Service Privacy…