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Category: Integration

find-f-x-y-0-pi-2-ln-x-y-sin-d-with-y-lt-x-2-find-f-2-3-3-find-f-2-3-

Question Number 45600 by maxmathsup by imad last updated on 14/Oct/18 $${find}\:{f}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({x}+{y}\:{sin}\theta\right){d}\theta\:\:{with}\:\:\mid{y}\mid<\mid{x}\mid \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}\left(\mathrm{2},\mathrm{3}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{f}\left(\sqrt{\mathrm{2}},\sqrt{\mathrm{3}}\right)\:. \\ $$ Commented by maxmathsup by imad…

Question-45561

Question Number 45561 by Sanjarbek last updated on 14/Oct/18 Commented by tanmay.chaudhury50@gmail.com last updated on 14/Oct/18 $${x}={sin}\theta\:\:\:\:{dx}={cos}\theta{d}\theta \\ $$$$\int\frac{{cos}\theta{d}\theta}{\:\sqrt{{cos}\theta}} \\ $$$$\int\sqrt{{cos}\theta}\:{d}\theta \\ $$$${wait}… \\ $$…

0-JS-dx-0-pi-2-sin-x-4-sin-2-x-4-sin-2-x-2-dx-

Question Number 111082 by john santu last updated on 02/Sep/20 $$\:\:\:\left[\int_{\mathrm{0}} ^{\infty} {JS}\:{dx}\:\right] \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{sin}\:\left({x}\right)\left(\mathrm{4}+\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)}{\left(\mathrm{4}−\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)^{\mathrm{2}} }\:{dx}\:? \\ $$ Commented by mathdave…