Question Number 50811 by ajfour last updated on 20/Dec/18 Commented by ajfour last updated on 20/Dec/18 $${Find}\:{distance}\:{between}\:{centres} \\ $$$${of}\:{the}\:{two}\:{equal}\:{ellipses}. \\ $$ Commented by ajfour last…
Question Number 181872 by srikanth2684 last updated on 01/Dec/22 $$\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}\frac{\mathrm{1}}{\mid{x}\mid}\:{dx} \\ $$ Answered by Frix last updated on 01/Dec/22 $$\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}\frac{{dx}}{\mid{x}\mid}=\underset{\mathrm{0}} {\overset{\mathrm{1}}…
Question Number 181857 by KINMATICS last updated on 01/Dec/22 Answered by hmr last updated on 01/Dec/22 $$\int_{\frac{\pi}{\mathrm{4}}} ^{\:\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\:\sqrt{\mathrm{2}}} \:\frac{{rcos}\left(\theta\right)}{{r}^{\mathrm{2}} }\:\:{r}\:{dr}\:{d}\theta \\ $$$$=\:\int_{\frac{\pi}{\mathrm{4}}} ^{\:\frac{\pi}{\mathrm{2}}}…
Question Number 116318 by Bird last updated on 03/Oct/20 $$\left.\mathrm{1}\right)\:{explicite}\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({a}+{x}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$$$\left.\mathrm{1}\left.\right)\:\mathrm{1}\right){calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{arctan}\left(\mathrm{1}+{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$$${and}\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left(\mathrm{3}+{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$…
Question Number 116311 by bemath last updated on 03/Oct/20 $$\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{3}}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{2x}}{\left(\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} }\:\mathrm{dx}\: \\ $$$$ \\ $$ Answered by bobhans last updated on 03/Oct/20 $$\mathrm{let}\:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{u}\:\mathrm{with}\:\begin{cases}{\mathrm{u}=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}\\{\mathrm{u}=\mathrm{0}}\end{cases}…
Question Number 181840 by srikanth2684 last updated on 01/Dec/22 $$\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}{ln}\:{x}\:{dx} \\ $$ Commented by mr W last updated on 01/Dec/22 $${question}\:{is}\:{wrong}.\: \\ $$$${for}\:\mathrm{ln}\:\left({x}\right)\:{to}\:{be}\:{defined},\:{x}>\mathrm{0}\:!…
Question Number 116299 by mnjuly1970 last updated on 02/Oct/20 $$\:\:\:…\:\:{advanced}\:\:{math}\:… \\ $$$$\:\:\:\:\:\:\:{evaluate}\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left[\frac{\mathrm{1}}{{ln}\left({x}\right)}\:+\frac{\mathrm{1}}{\mathrm{1}−{x}}\:\right]^{\mathrm{2}} {dx}=??? \\ $$$$\:\:\:\:\:\:\:{m}.{n} \\ $$ Terms of…
Question Number 116272 by mindispower last updated on 02/Oct/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({x}^{\mathrm{2}} +{ln}^{\mathrm{2}} \left({cos}\left({x}\right)\right)\right){dx}=\pi{ln}\left({ln}\left(\mathrm{2}\right)\right) \\ $$$${posted}\:{Quation}\: \\ $$$${not}\:{solved}\:{yet}\:{i}\:{hop}\:{someon}\:{Giv}\:{idea}\:{for} \\ $$$${this}\:{one}\:{thank}\:{you} \\ $$ Answered by mathdave…
Question Number 181793 by zainaltanjung last updated on 30/Nov/22 $$\mathrm{Please}\:\mathrm{Calculate}\:\mathrm{this}\:\mathrm{problem} \\ $$$$\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{dx}\:\underset{\mathrm{x}^{\mathrm{2}} } {\overset{\sqrt{\mathrm{x}}} {\int}}\:\mathrm{dy}=…. \\ $$ Commented by Frix last updated on…
Question Number 181792 by zainaltanjung last updated on 30/Nov/22 $$\mathrm{Please}\:\mathrm{Calculate}\:\mathrm{this}\:\mathrm{integration} \\ $$$$\mathrm{2}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{dx}\:\underset{\mathrm{2x}} {\overset{\left(\mathrm{2x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} } {\int}}\:\mathrm{dy} \\ $$ Commented by Frix last updated on…