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Category: Integration

Question-75027

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}}…

What-s-the-relationship-between-Dirichlet-s-function-with-s-function-That-is-n-0-1-n-2n-1-s-with-n-1-1-n-s-

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…

x-2-1-x-2-dx-

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-140490

Question Number 140490 by benjo_mathlover last updated on 08/May/21 Commented by john_santu last updated on 08/May/21 $$\frac{\pi}{\mathrm{2}}\:\left(\sqrt{\mathrm{2}\sqrt{\mathrm{2}}+\mathrm{2}}\:−\mathrm{2}\:\right)\:\approx\:\mathrm{0}.\mathrm{31} \\ $$ Answered by MJS_new last updated on…