Question Number 65319 by hovea cw last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 28/Jul/19 $${those}\:{integrals}\:{are}\:{solved}\:\:{see}\:{the}\:{platform}. \\ $$ Commented by mathmax…
Question Number 130844 by mnjuly1970 last updated on 29/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:\:{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{3}}} \frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{cos}^{\mathrm{2}} \left({x}\right)}}\:=\frac{\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}} \sqrt{\pi}}{\:\sqrt{\mathrm{3}}} \\ $$ Answered by Dwaipayan Shikari last…
Question Number 65307 by divyajyoti last updated on 28/Jul/19 $$\int\frac{\left(\mathrm{4}{x}+\mathrm{3}\right){dx}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{3}}}\:=\:?\: \\ $$ Answered by divyajyoti last updated on 28/Jul/19 $$=\int\frac{{dt}}{\:\sqrt{{t}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int\frac{{dx}}{\:\sqrt{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\sqrt{\mathrm{7}}}{\mathrm{2}}\right)^{\mathrm{2}} }} \\ $$$$=\mathrm{2}\sqrt{\mathrm{2}{x}^{\mathrm{2}}…
Question Number 130845 by mnjuly1970 last updated on 29/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:{calculate}:: \\ $$$$\:\:\:{lim}_{\:{n}\rightarrow\infty} \underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{k}}{\mathrm{2}{n}^{\mathrm{2}} +{k}}\:=? \\ $$$$ \\ $$ Answered by Ar…
Question Number 130835 by mathmax by abdo last updated on 29/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{4}} \right)}{\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 65293 by mathmax by abdo last updated on 27/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}−{a}}\:\:{with}\:{a}\:\in{C} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}}\:\:{and}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{6}} \:+\mathrm{1}} \\ $$$${by}\:{using}\:{the}\:{decomposition}\:{inside}\:{C}\left({x}\right). \\…
Question Number 65290 by mathmax by abdo last updated on 27/Jul/19 $${f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{{x}+{e}^{{t}} }\:\:\:{with}\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{aexplicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{2}+{e}^{{t}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 65288 by mathmax by abdo last updated on 27/Jul/19 $$\left.\mathrm{1}\right)\:{let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{3}} \:+{x}^{\mathrm{3}} }\:\:\:{with}\:{x}>\mathrm{0} \\ $$$${calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{3}} \:+{x}^{\mathrm{3}} \right)^{\mathrm{2}} }…
Question Number 65287 by mathmax by abdo last updated on 27/Jul/19 $${let}\:{f}\left({x}\right)\:={x}\mid{x}\mid\:\:\:\:\mathrm{2}\pi\:{periodic}\:\:{odd} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{series} \\ $$ Commented by mathmax by abdo last updated on 28/Jul/19…
Question Number 65286 by mathmax by abdo last updated on 27/Jul/19 $$\left.\mathrm{1}\right){find}\:\:\:{f}\left({a}\right)=\int_{−\infty} ^{+\infty} \:\:{e}^{−{ax}^{\mathrm{2}} } {cos}\left(\mathrm{3}−{x}^{\mathrm{2}} \right){dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\mathrm{3}{x}^{\mathrm{2}} } {cos}\left(\mathrm{3}−{x}^{\mathrm{2}} \right){dx} \\…