Question Number 36186 by prof Abdo imad last updated on 30/May/18 $${find}\:{nature}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \sqrt{{t}}\:{sin}\left({t}^{\mathrm{2}} \right){dt}\:. \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 36187 by prof Abdo imad last updated on 30/May/18 $${let}\:{I}_{{n}} \left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}\:{sin}\left({t}\right)}{\left({t}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \right)^{{n}} }{dt}\: \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{relation}\:{between}\:{I}_{{n}+\mathrm{1}} \:\:{and}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{\mathrm{2}} \left({x}\right)\:{and}\:{I}_{\mathrm{3}} \left({x}\right)\:…
Question Number 36184 by prof Abdo imad last updated on 30/May/18 $${study}\:{the}\:{convergence}\:{of}\:\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{cos}\left({t}\right)}{\:\sqrt{{t}}}{dt} \\ $$ Commented by maxmathsup by imad last updated on 19/Aug/18…
Question Number 36185 by prof Abdo imad last updated on 30/May/18 $${study}\:{the}\:{vonvergence}\:{of}\: \\ $$$$\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{e}^{−\frac{\mathrm{1}}{{t}}} \:−{cos}\left(\frac{\mathrm{1}}{{t}}\right)}{{t}}{dt} \\ $$ Commented by maxmathsup by imad last…
Question Number 36183 by prof Abdo imad last updated on 30/May/18 $${calculate}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:{arctan}\left(\frac{\mathrm{1}}{{t}}\right){dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 36180 by prof Abdo imad last updated on 30/May/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left({t}\right)}{\left(\mathrm{1}+{t}\right)^{\mathrm{2}} }{dt} \\ $$ Commented by prof Abdo imad last updated on…
Question Number 36181 by prof Abdo imad last updated on 30/May/18 $${let}\:{I}\left(\xi\right)\:\:=\:\int_{\xi} ^{\mathrm{1}−\xi} \:\:\:\frac{{dt}}{\mathrm{1}−\left({t}−\xi\right)^{\mathrm{2}} } \\ $$$${find}\:{lim}_{\xi\rightarrow\mathrm{0}^{+} } \:\:\:{I}\left(\xi\right) \\ $$ Commented by maxmathsup by…
Question Number 36182 by prof Abdo imad last updated on 30/May/18 $${calculate}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{{dt}}{{t}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 36167 by abdo mathsup 649 cc last updated on 29/May/18 $${let}\:{give}\:\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{i}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{extract}\:{Re}\left({I}\right)\:{and}\:{Im}\left({I}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{I} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{Re}\left({I}\right)\:{and}\:{Im}\left({I}\right)\:. \\ $$…
Question Number 167223 by cortano1 last updated on 10/Mar/22 $$\:\:\int\:\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{3x}\right)\:\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{5x}\right)\:\mathrm{dx}=? \\ $$ Commented by greogoury55 last updated on 10/Mar/22 $$\:\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{3}{x}\right)=\frac{\mathrm{3sin}\:\left(\mathrm{3}{x}\right)−\mathrm{sin}\:\left(\mathrm{9}{x}\right)}{\mathrm{4}} \\ $$$$\:\mathrm{cos}\:^{\mathrm{4}}…