Category: Integration

Question Number 33170 by prof Abdo imad last updated on 11/Apr/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mid{sinx}\mid}{{x}}\:{dx}\:{is}\:{divergent}. \\ $$ Commented by prof Abdo imad last updated on 13/Apr/18…

Question Number 164231 by Zaynal last updated on 15/Jan/22 $$\int_{−\infty} ^{\infty} \:−\frac{\mathrm{1}}{\mathrm{3}}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(\frac{\frac{\:^{\mathrm{4}} \boldsymbol{\mathrm{log}}\:\mathrm{3}.^{\mathrm{4}} \boldsymbol{\mathrm{log}}\:\mathrm{6}}{\:\:^{\mathrm{4}} \boldsymbol{\mathrm{log}}\:\mathrm{9}.^{\mathrm{8}} \boldsymbol{\mathrm{log}}\:\mathrm{2}+\:^{\mathrm{4}} \boldsymbol{\mathrm{log}}\:\mathrm{9}.^{\mathrm{8}} \boldsymbol{\mathrm{log}}\:\mathrm{3}}}{\frac{\:^{\mathrm{9}} \boldsymbol{\mathrm{log}}\:\mathrm{4}.^{\mathrm{2}} \boldsymbol{\mathrm{log}}\mathrm{27}+^{\mathrm{3}} \boldsymbol{\mathrm{log}}\:\mathrm{81}}{\:^{\mathrm{2}} \boldsymbol{\mathrm{log}}\:\mathrm{64}−^{\mathrm{2}} \boldsymbol{\mathrm{log}}\:\mathrm{8}}}\right)\boldsymbol{\mathrm{dxdy}}…

Question Number 98679 by  M±th+et+s last updated on 15/Jun/20 $${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{3}+\mathrm{2}\sqrt{{x}}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}}{dx}=\mathrm{4}.\mathrm{13049}\: \\ $$ Commented by MJS last updated on 15/Jun/20 $${t}=\sqrt{{x}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}{dt}…

Question Number 98672 by  M±th+et+s last updated on 15/Jun/20 $$\int_{\mathrm{0}} ^{\mathrm{4}} \int_{\mathrm{0}} ^{\frac{{x}}{\mathrm{4}}} {e}^{{x}^{\mathrm{2}} } \:{dx}\:{dy} \\ $$ Answered by Ar Brandon last updated on…

Question Number 33129 by prof Abdo imad last updated on 10/Apr/18 $$\left.\mathrm{1}\right){find}\:{the}\:{value}\:{of}\:\:\:{u}_{{n}} =\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left({nx}\right)}{\mathrm{4}\:+{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} \:. \\ $$ Commented by prof Abdo…