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Category: Integration

D-x-y-x-y-2-D-e-x-y-dydx-

Question Number 127157 by kaivan.ahmadi last updated on 27/Dec/20 $${D}=\left\{\left({x},{y}\right):\mid{x}\mid+\mid{y}\mid\leqslant\mathrm{2}\right\} \\ $$$$\int\underset{{D}} {\int}{e}^{{x}+{y}} {dydx}=? \\ $$ Answered by Ar Brandon last updated on 27/Dec/20 $$\mathrm{D}=\left\{\left(\mathrm{x},\:\mathrm{y}\right)\::\:\mid\mathrm{x}\mid+\mid\mathrm{y}\mid\leqslant\mathrm{2}\right\}…

arcsin-x-2-dx-

Question Number 127110 by benjo_mathlover last updated on 26/Dec/20 $$\:\:\int\:\left(\mathrm{arcsin}\:{x}\right)^{\mathrm{2}} \:{dx}\:=? \\ $$ Answered by liberty last updated on 27/Dec/20 $$\:{letting}\:\mathrm{arcsin}\:{x}\:=\:\ell\:\Rightarrow{x}\:=\:\mathrm{sin}\:\ell\:\wedge\:{dx}\:=\:\mathrm{cos}\:\ell\:{d}\ell \\ $$$${I}=\:\int\:\ell^{\mathrm{2}} \mathrm{cos}\:\ell\:{d}\ell\:=\:\ell^{\mathrm{2}} \mathrm{sin}\:\ell\:+\mathrm{2}\ell\:\mathrm{cos}\:\ell−\mathrm{2sin}\:\ell\:+\:{c}…

2-4-ln-9-6-x-ln-9-x-ln-3-x-dx-

Question Number 61566 by aliesam last updated on 04/Jun/19 $$\int_{\mathrm{2}} ^{\mathrm{4}} \:\frac{\sqrt{{ln}\left(\mathrm{9}−\left(\mathrm{6}−{x}\right)\right.}}{\:\sqrt{{ln}\left(\mathrm{9}−{x}\right)}\:+\:\sqrt{{ln}\left(\mathrm{3}−{x}\right)}}\:{dx} \\ $$ Answered by tanmay last updated on 04/Jun/19 $${i}\:{think}\:{question}\:{is}\:{typo}\:{error}.. \\ $$$$\int_{{a}} ^{{b}}…

sin-12x-8-dx-

Question Number 192634 by pascal889 last updated on 23/May/23 $$\int\boldsymbol{{sin}}\left(\mathrm{12}{x}\:+\mathrm{8}\:\right){dx} \\ $$ Answered by Subhi last updated on 23/May/23 $$−\frac{\mathrm{1}}{\mathrm{12}}\int−\mathrm{12}{sin}\left(\mathrm{12}{x}+\mathrm{8}\right){dx} \\ $$$$−\frac{\mathrm{1}}{\mathrm{12}}{cos}\left(\mathrm{12}{x}+\mathrm{8}\right)+{c} \\ $$ Commented…

calculate-f-a-W-x-ay-e-x-e-ay-dxdy-with-W-a-x-y-R-2-x-0-y-0-x-ay-1-a-gt-0-

Question Number 61534 by maxmathsup by imad last updated on 04/Jun/19 $${calculate}\:{f}\left({a}\right)\:=\int\int_{{W}} \:\left({x}+{ay}\right){e}^{−{x}} \:{e}^{−{ay}} {dxdy}\:{with} \\ $$$${W}_{{a}} =\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}\geqslant\mathrm{0}\:,{y}\geqslant\mathrm{0}\:\:\:,\:{x}+{ay}\:\leqslant\mathrm{1}\:\right\}\:\:\:{a}>\mathrm{0} \\ $$ Terms of Service Privacy…

let-U-n-0-x-2n-1-x-4-dx-with-n-integr-natural-and-n-1-1-calculate-U-n-interms-of-n-2-find-lim-n-n-2-U-n-3-study-the-serie-U-n-

Question Number 61530 by maxmathsup by imad last updated on 04/Jun/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}^{−\mathrm{2}{n}} }{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:\:\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}} \:{U}_{{n}} \\…