Menu Close

Category: Integration

mathematical-analysis-prove-that-0-1-x-8-1-ln-x-x-10-1-dx-pi-2-2-25-m-n-july-1970-

Question Number 115111 by mnjuly1970 last updated on 23/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{mathematical}\:\:{analysis}…\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left({x}^{\mathrm{8}} +\mathrm{1}\right){ln}\left({x}\right)}{{x}^{\mathrm{10}} −\mathrm{1}}\:{dx}=\frac{\pi^{\mathrm{2}} \varphi^{\mathrm{2}} }{\mathrm{25}}\:\:\checkmark \\…

0-pi-2-cos-x-1-sin-x-dx-

Question Number 115071 by bemath last updated on 23/Sep/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{1}−\mathrm{sin}\:{x}}}\:{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 23/Sep/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{cosx}}{\:\sqrt{\mathrm{1}−{sinx}}}{dx}…

nice-calculus-a-b-c-d-N-and-1-a-1-b-1-c-1-d-1-2-find-

Question Number 115058 by mnjuly1970 last updated on 23/Sep/20 $$\:\:\:\:\:\:\:….\:\:{nice}\:\:{calculus}\:… \\ $$$$\:\:\:\:\:\:{a}\:,\:{b}\:,\:{c}\:,\:{d}\:\:\in\mathbb{N}\:{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}+\frac{\mathrm{1}}{{d}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{find}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{max}\left({a}+{b}+{c}+{d}\right)\:=??? \\ $$$$\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}… \\ $$ Answered…

nice-calculus-evaluation-0-1-log-1-x-log-1-x-m-n-july-197o-

Question Number 115055 by mnjuly1970 last updated on 23/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:{evaluation}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\chi=\int_{\mathrm{0}} ^{\:\mathrm{1}} {log}\left(\mathrm{1}−{x}\right).{log}\left(\mathrm{1}+{x}\right)\:=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{197}{o}… \\ $$$$\: \\ $$ Answered…

x-2-x-2-2-dx-

Question Number 115051 by gab last updated on 23/Sep/20 $$\int{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} −\mathrm{2}}{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 23/Sep/20 $$\int\mathrm{2}\sqrt{\mathrm{2}}{sin}^{\mathrm{2}} \theta{cos}\theta\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \theta−\mathrm{2}}\:{d}\theta\:\:\:\:\:\:\:\:\:\:\:{x}=\sqrt{\mathrm{2}}{sin}\theta\:\Rightarrow\mathrm{1}=\sqrt{\mathrm{2}}\:{cos}\theta\frac{{d}\theta}{{dx}}\:…

pi-2-pi-2-sec-x-cos-x-dx-

Question Number 115030 by bobhans last updated on 23/Sep/20 $$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\sqrt{\mathrm{sec}\:{x}−\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$ Answered by bemath last updated on 23/Sep/20 $$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\sqrt{\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}}{\mathrm{cos}\:{x}}}\:{dx}\:=\:\underset{−\frac{\pi}{\mathrm{2}}}…

nice-math-if-y-cos-2x-1-2-then-prove-y-y-3y-5-m-n-july-1970-

Question Number 115000 by mnjuly1970 last updated on 22/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:\:{math}… \\ $$$$ \\ $$$$\:{if}\:\:{y}\:=\left({cos}\left(\mathrm{2}{x}\right)\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} \:{then} \\ $$$${prove}\:::\:\:\:{y}+{y}^{''} =\:\mathrm{3}{y}^{\mathrm{5}} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}… \\ $$ Answered…