Question Number 122469 by benjo_mathlover last updated on 17/Nov/20 Commented by benjo_mathlover last updated on 17/Nov/20 $${i}'{m}\:{forgot}\:{the}\:{formula}\:{the}\:\:{average}\:{rate}\:{of} \\ $$$${change}\:{of}\:{the}\:{function}.\:{is}\:{it}\: \\ $$$${A}\left({x}\right)\:=\:\frac{\mathrm{1}}{{b}−{a}}\:\underset{{a}} {\overset{{b}} {\int}}\:{f}\left({x}\right)\:{dx}\:? \\ $$…
Question Number 56931 by turbo msup by abdo last updated on 26/Mar/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad…
Question Number 187993 by mathlove last updated on 24/Feb/23 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt[{\mathrm{3}}]{\frac{{sin}\mathrm{3}{x}}{{sin}\mathrm{2}{y}}}{dxdy}=\frac{\pi}{\mathrm{2}\sqrt{\mathrm{3}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 122461 by benjo_mathlover last updated on 17/Nov/20 $$\:\int\:\frac{{x}}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{3}} +{b}^{\mathrm{2}} \right)}\:? \\ $$ Commented by liberty last updated on 17/Nov/20 $$\mathrm{Ostrogradsky}..\mathrm{method}.\: \\…
Question Number 122432 by Lordose last updated on 17/Nov/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 122430 by benjo_mathlover last updated on 17/Nov/20 $$\:\int\:\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }+{x}^{\mathrm{2}} −\mathrm{4}}\:{dx}\: \\ $$ Answered by liberty last updated on 17/Nov/20 $$\:\mathrm{let}\:\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:=\:\omega\:\wedge\:\mathrm{x}^{\mathrm{2}} −\mathrm{4}\:=−\omega^{\mathrm{2}}…
Question Number 122397 by Ar Brandon last updated on 16/Nov/20 $$\mathrm{a}\backslash\int\frac{\mathrm{2x}+\mathrm{1}}{\mathrm{1}+\mathrm{x}}\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}\mathrm{dx}\:\:\:\:\:\:\:\:\mathrm{c}\backslash\int\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}}+\sqrt[{\mathrm{3}}]{\mathrm{x}}} \\ $$$$\mathrm{b}\backslash\int\frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}−\mathrm{1}}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{d}\backslash\int\frac{\mathrm{dx}}{\:\left(\mathrm{1}+\mathrm{x}\right)\sqrt{\mathrm{1}+\mathrm{x}+\mathrm{x}^{\mathrm{2}} }} \\ $$ Answered by Dwaipayan Shikari last updated on 16/Nov/20 $$\int\frac{{dx}}{{x}+\sqrt{{x}−\mathrm{1}}}…
Question Number 122366 by rs4089 last updated on 16/Nov/20 Answered by mathmax by abdo last updated on 16/Nov/20 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{sin}\left(\mathrm{sinx}\right)}{\mathrm{x}}\mathrm{e}^{\mathrm{cosx}} \mathrm{dx}\:\:\mathrm{the}\:\mathrm{function}\:\mathrm{under}\:\mathrm{integral}\:\mathrm{is}\:\mathrm{even}\:\Rightarrow \\ $$$$\mathrm{2I}=\int_{−\infty} ^{+\infty}…
Question Number 56829 by maxmathsup by imad last updated on 24/Mar/19 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({t}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{with}\:{t}\geqslant\mathrm{0} \\ $$$${find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right)\: \\ $$ Answered by Smail last updated…
Question Number 56827 by maxmathsup by imad last updated on 24/Mar/19 $${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{3}} \\ $$ Commented by maxmathsup by imad last updated…