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Category: Integration

let-A-n-W-n-e-xy-x-2-y-2-dxdy-with-W-n-1-n-n-1-n-n-1-find-A-n-interms-of-n-2-determine-lim-n-A-n-

Question Number 56938 by maxmathsup by imad last updated on 26/Mar/19 $${let}\:{A}_{{n}} =\int\int_{{W}_{{n}} } {e}^{−{xy}} \sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy}\:\:\:{with}\:{W}_{{n}} =\left[\frac{\mathrm{1}}{{n}},{n}\left[×\left[\frac{\mathrm{1}}{{n}},{n}\left[\right.\right.\right.\right. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{A}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}}…

calculate-dx-x-1-3-x-2-3x-2-2-find-the-value-of-2-dx-x-1-3-x-2-3x-2-

Question Number 56939 by maxmathsup by imad last updated on 26/Mar/19 $${calculate}\:\int\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{3}{x}\:+\mathrm{2}\right)} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{2}} ^{+\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}\right)} \\ $$ Commented by turbo…

1-calculate-U-n-0-x-3-2x-1-e-n-x-dx-with-n-integr-natural-and-n-1-2-find-nature-of-U-n-

Question Number 56935 by maxmathsup by imad last updated on 27/Mar/19 $$\mathrm{1}.\:{calculate}\:\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\left({x}^{\mathrm{3}} −\mathrm{2}{x}+\mathrm{1}\right){e}^{−{n}\left[{x}\right]} {dx}\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\mathrm{2}.\:{find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by maxmathsup by…

Question-122469

Question Number 122469 by benjo_mathlover last updated on 17/Nov/20 Commented by benjo_mathlover last updated on 17/Nov/20 $${i}'{m}\:{forgot}\:{the}\:{formula}\:{the}\:\:{average}\:{rate}\:{of} \\ $$$${change}\:{of}\:{the}\:{function}.\:{is}\:{it}\: \\ $$$${A}\left({x}\right)\:=\:\frac{\mathrm{1}}{{b}−{a}}\:\underset{{a}} {\overset{{b}} {\int}}\:{f}\left({x}\right)\:{dx}\:? \\ $$…