Question Number 34265 by math khazana by abdo last updated on 03/May/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\mathrm{2}{t}} \:{sin}\left(\left[{t}\right]\right)\:{dt}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 165339 by mnjuly1970 last updated on 30/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:#\:{Advanced}\:\:\:{Calculus}\:#\:\:\: \\ $$$$\:\:\:\:\:\mathrm{L}{et}\:,\:\:{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{Q}\:\:{is}\:\:{a}\:\:{continuous} \\ $$$$\:\:\:\:\:\:{function}\:\:.\:{prove}\:{that}\:\:''\:{f}\:''\:{is}\:{a} \\ $$$$\:\:\:\:\:\:\:{constant}\:{function}\:.\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$$$\:\:\:\:\:\:\:\ast\:{Adopted}\:{from}\:{mathematical}\:{analysis}\:{book}\:\:\ast\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−−−−−−− \\ $$$$ \\…
Question Number 34264 by math khazana by abdo last updated on 03/May/18 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\mathrm{2}\left[{t}\right]} {sint}\:{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34262 by math khazana by abdo last updated on 03/May/18 $${find}\:{the}\:{nature}\:{of}\:\int_{\mathrm{2}} ^{+\infty} \left(\sqrt{\mathrm{1}+{t}^{\mathrm{2}} +{t}^{\mathrm{4}} \:}\:\:−{t}\:\:^{\mathrm{3}} \sqrt{{t}^{\mathrm{3}} +{at}}\right){dt} \\ $$$${a}\in{R}\:. \\ $$ Terms of…
Question Number 34260 by math khazana by abdo last updated on 03/May/18 $${let}\:{give}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:{F}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{lnt}}{{t}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{G}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{aln}\left({t}\right)}{\left({t}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 34261 by math khazana by abdo last updated on 03/May/18 $${study}\:{the}\:{convergence}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{t}−{sint}}{{t}^{{a}} }{dt}\:{with}\:{a}\:{real}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 165329 by mnjuly1970 last updated on 30/Jan/22 $$ \\ $$$$\:\:\:\:{prove}\:\:\:\:\:\:\:\:\:\:\left(\:{n}\in\:\mathbb{N}\:\right) \\ $$$$\:\:\:\:\mathrm{3}\left({n}+\mathrm{1}\right)\:\mid\:{n}^{\:\mathrm{3}} \:+\:\left({n}+\mathrm{1}\right)^{\:\mathrm{3}} +\:\left({n}+\mathrm{2}\:\right)^{\:\mathrm{3}} \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 34257 by math khazana by abdo last updated on 03/May/18 $${find}\:{f}\left({x}\right)=\:\int_{\mathrm{1}} ^{{x}} \:\:\:\:\frac{{dt}}{{t}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}\:=\int_{\mathrm{1}} ^{+\infty} \:\:\:\:\frac{{dt}}{{t}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }} \\ $$ Terms of…
Question Number 34254 by math khazana by abdo last updated on 03/May/18 $${find}\:{I}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 34255 by math khazana by abdo last updated on 03/May/18 $${find}\:\:{g}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+\mathrm{3}{t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:. \\ $$…