Menu Close

Category: Integration

Question-159233

Question Number 159233 by mnjuly1970 last updated on 14/Nov/21 Answered by mindispower last updated on 16/Nov/21 $${A}_{\mathrm{2}{n}} =\underset{{k}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{1}}{\left(\mathrm{2}{k}\right)^{\mathrm{2}{n}} }=\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}{n}} }.\zeta\left(\mathrm{2}{n}\right) \\ $$$$\frac{\frac{\zeta\left(\mathrm{2}{n}\right)}{\mathrm{2}^{\mathrm{2}{n}} }}{\mathrm{2}{n}\left(\mathrm{2}{n}+\mathrm{1}\right)}=−\frac{\zeta\left(\mathrm{2}{n}\right)}{\mathrm{2}^{\mathrm{2}{n}} \left(\mathrm{2}{n}+\mathrm{1}\right)}+\frac{\zeta\left(\mathrm{2}{n}\right)}{\mathrm{2}^{\mathrm{2}{n}}…

find-the-value-of-W-ln-1-x-y-dxdy-with-W-x-y-R-2-x-y-1-and-x-0-and-y-0-

Question Number 28161 by abdo imad last updated on 21/Jan/18 $${find}\:{the}\:{value}\:{of}\:\int\int_{{W}} {ln}\left(\mathrm{1}+{x}+{y}\right){dxdy}\:{with} \\ $$$${W}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}+{y}\leqslant\mathrm{1}\:{and}\:{x}\geqslant\mathrm{0}\:{and}\:{y}\geqslant\mathrm{0}\right\}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

t-2-i-cos-2tj-e-t-k-dt-

Question Number 93683 by i jagooll last updated on 14/May/20 $$\int\:\left(\mathrm{t}^{\mathrm{2}} \boldsymbol{\mathrm{i}}\:+\mathrm{cos}\:\mathrm{2t}\boldsymbol{\mathrm{j}}\:+\mathrm{e}^{−\mathrm{t}} \boldsymbol{\mathrm{k}}\right)\:\mathrm{dt}\: \\ $$ Answered by john santu last updated on 14/May/20 $$=\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{t}^{\mathrm{3}} \:\overset{\rightarrow}…