Question Number 140615 by bramlexs22 last updated on 10/May/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{common}\: \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{12x}\:\mathrm{and} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\mathrm{24x}\:. \\ $$ Answered by EDWIN88 last updated on…
Question Number 140614 by bramlexs22 last updated on 10/May/21 $$\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\:\left(\mathrm{sin}\:\mathrm{x}\right)\:\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}\:=?\: \\ $$$$ \\ $$ Answered by bemath last updated on 10/May/21 Answered…
Question Number 9520 by ridwan balatif last updated on 12/Dec/16 $$\int\frac{\mathrm{sinxcosx}}{\mathrm{4}+\mathrm{sin}^{\mathrm{4}} \mathrm{x}}\mathrm{dx}=…? \\ $$ Answered by mrW last updated on 12/Dec/16 $$\mathrm{u}=\mathrm{sin}\:\mathrm{x} \\ $$$$\mathrm{du}=\mathrm{cos}\:\mathrm{xdx} \\…
Question Number 140588 by mnjuly1970 last updated on 09/May/21 $$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{Advanced}\:….\bigstar\bigstar\bigstar….{Calculus}……. \\ $$$$\:\:\:\:\:\:\:\:{evaluation}\:{the}\:{value}\:{of}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\::=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}} \left({x}\right).{ln}\left({sin}\left({x}\right)\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:{solution}:: \\ $$$$\:\:\:\:\:\:\:\xi\:\left({a}\right):=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}+{a}}…
Question Number 75034 by chess1 last updated on 06/Dec/19 Answered by Kunal12588 last updated on 06/Dec/19 $${y}={x}^{{x}^{{x}^{{x}} } } \\ $$$${log}\:{y}\:={x}^{{x}^{{x}} } {log}\:{x} \\ $$$${log}\:\left({log}\:{y}\right)\:=\:{x}^{{x}}…
Question Number 75027 by chess1 last updated on 06/Dec/19 Commented by mathmax by abdo last updated on 06/Dec/19 $${x}+{z}=\mathrm{3}\:\Rightarrow\mathrm{0}\leqslant{x}\leqslant\mathrm{3}\:{and}\:\mathrm{0}\leqslant{z}\leqslant\mathrm{3}\:\:\:{we}\:{have}\:\:\mathrm{0}\leqslant{y}\leqslant\mathrm{2}\:\Rightarrow \\ $$$$\int\int\int\:\:\frac{{dxdydz}}{\left({x}+{y}+{z}\right)^{\mathrm{3}} }\:=\int_{\mathrm{0}} ^{\mathrm{3}} \left(\:\int_{{o}} ^{\mathrm{2}}…
Question Number 140554 by qaz last updated on 09/May/21 $${What}'{s}\:{the}\:{relationship}\:{between}\:{Dirichlet}\:\beta\left({s}\right)\:{function}\:{with} \\ $$$$\zeta\left({s}\right)\:{function}\:?\:{That}\:{is}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{{s}} }\:\:{with}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{{s}} }. \\ $$ Commented by qaz last…
Question Number 9482 by sou1618 last updated on 10/Dec/16 $${find}\:\:{F}_{{n}} \left(−\mathrm{1}\right)\:{or}\:{F}_{{n}} \left({x}\right). \\ $$$${n}=\mathrm{1},\mathrm{2},\mathrm{3}…… \\ $$$${F}_{{n}} \left({x}\right)=\int\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{{n}} {dx} \\ $$ Commented by sou1618 last…
Question Number 9467 by tawakalitu last updated on 09/Dec/16 $$\int\mathrm{x}^{\mathrm{2}} \left(\sqrt{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} }\right)\:\mathrm{dx} \\ $$ Answered by mrW last updated on 09/Dec/16 $$\mathrm{x}=\mathrm{sin}\:\mathrm{t} \\ $$$$\mathrm{dx}=\mathrm{cos}\:\mathrm{t}\:\mathrm{dt} \\…
Question Number 74997 by chess1 last updated on 05/Dec/19 Commented by chess1 last updated on 05/Dec/19 $$\mathrm{answer}:\:\mathrm{A} \\ $$ Answered by mind is power last…