Question Number 121983 by Dwaipayan Shikari last updated on 13/Nov/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {sin}^{{n}} {x}\:{dx}\:\left({In}\:{closed}\:{form}\right)\:\:\left({n}\in\mathbb{N}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 13/Nov/20 $${I}\:{have}\:{found}…
Question Number 187504 by Noorzai last updated on 18/Feb/23 Commented by mr W last updated on 18/Feb/23 $${when}\:{you}\:{even}\:{understand}\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\:{x}}{{x}^{\mathrm{6}} −\mathrm{1}}{dx}, \\ $$$${do}\:{you}\:{really}\:{need}\:{help}\:{even}\:{for}\:{this}\: \\ $$$${kindergarten}\:{question}?…
Question Number 187498 by Noorzai last updated on 18/Feb/23 Answered by cortano12 last updated on 18/Feb/23 $$\:{x}=\frac{\mathrm{5}}{\mathrm{8}}+\frac{\mathrm{7}}{\mathrm{17}}+\frac{\mathrm{3}}{\mathrm{11}} \\ $$$$\:{x}=\frac{\mathrm{3}}{\mathrm{8}}+\frac{\mathrm{10}}{\mathrm{17}}+\frac{\mathrm{8}}{\mathrm{11}}+\frac{\mathrm{2}}{\mathrm{8}}−\frac{\mathrm{3}}{\mathrm{17}}−\frac{\mathrm{5}}{\mathrm{11}} \\ $$$$\:\Rightarrow\frac{\mathrm{3}}{\mathrm{8}}+\frac{\mathrm{10}}{\mathrm{17}}+\frac{\mathrm{8}}{\mathrm{11}}={x}−\left(\frac{\mathrm{2}}{\mathrm{8}}−\frac{\mathrm{3}}{\mathrm{17}}−\frac{\mathrm{5}}{\mathrm{11}}\right) \\ $$ Terms of…
Question Number 121914 by Dwaipayan Shikari last updated on 12/Nov/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({sin}\theta\right)^{−\frac{\mathrm{1}}{{n}}} {d}\theta \\ $$ Commented by Dwaipayan Shikari last updated on 12/Nov/20 $$\frac{\mathrm{1}}{\mathrm{2}}.\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}{n}}\right)\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)}{\Gamma\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{n}}\right)}\:\:\:\left({n}>\mathrm{1}\right)…
Question Number 56378 by tanmay.chaudhury50@gmail.com last updated on 15/Mar/19 Commented by tanmay.chaudhury50@gmail.com last updated on 15/Mar/19 $${my}\:{newfriend}… \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on…
Question Number 187433 by Mastermind last updated on 17/Feb/23 $$\mathrm{Prove}\:\mathrm{that}\:\bigtriangledown×\bigtriangledown\phi=\mathrm{0}.\:\mathrm{If}\:\phi\:\mathrm{is} \\ $$$$\mathrm{assumed}\:\mathrm{to}\:\mathrm{be}\:\mathrm{continous}\:\mathrm{and} \\ $$$$\mathrm{having}\:\mathrm{continous}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second} \\ $$$$\mathrm{order}\:\mathrm{derivatives}. \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$ Answered by aleks041103…
Question Number 56358 by harish 12@g last updated on 15/Mar/19 $$\int_{\mathrm{0}} ^{\infty} \left(\mathrm{cot}^{−\mathrm{1}} {x}\right)^{\mathrm{2}} {dx} \\ $$$$ \\ $$ Commented by MJS last updated on…
Question Number 56321 by Tawa1 last updated on 14/Mar/19 $$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\:\:\:\:\:\:\mathrm{x}\:\sqrt{\mathrm{x}}\:\:+\:\mathrm{y}\sqrt{\mathrm{y}}\:\:=\:\mathrm{182}\:\:\:\:\:\:…..\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\mathrm{x}\:\sqrt{\mathrm{y}}\:\:+\:\mathrm{y}\sqrt{\mathrm{x}}\:\:=\:\mathrm{183}\:\:\:\:\:\:…..\:\left(\mathrm{ii}\right) \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 14/Mar/19 $${x}={a}^{\mathrm{2}} \:\:\:{y}={b}^{\mathrm{2}}…
Question Number 56282 by Tawa1 last updated on 13/Mar/19 Commented by mr W last updated on 13/Mar/19 $$\mathrm{sin}^{\mathrm{2}} \:\mathrm{1}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}°+…+\mathrm{sin}^{\mathrm{2}} \:\mathrm{44}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{45}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{46}°+…+\mathrm{sin}^{\mathrm{2}} \:\mathrm{88}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{89}°+\mathrm{sin}^{\mathrm{2}}…
Question Number 56243 by Kunal12588 last updated on 12/Mar/19 $$\mathrm{6}/\mathrm{2}×\mathrm{5} \\ $$$$\:{which}\:{one}\:{correct} \\ $$$$\mathrm{6}/\mathrm{2}×\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\mathrm{6}/\mathrm{2}×\mathrm{5} \\ $$$$=\mathrm{3}×\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{6}/\mathrm{10} \\ $$$$=\mathrm{15}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{0}.\mathrm{6} \\ $$ Answered by MJS last updated…