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Category: Integration

let-D-n-x-y-R-2-x-y-1-n-n-1-find-the-value-of-D-n-e-x-2-y-2-dxdy-2-calculate-0-e-x-2-dx-

Question Number 51994 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{D}_{{n}} =\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} \:\:/\left({x},{y}\right)\in\left[\frac{\mathrm{1}}{{n}}\:,{n}\left[\:\right\}\right.\right. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\int\int_{{D}_{{n}} } \:\:\:\:\:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } {dxdy} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{+\infty} \:{e}^{−{x}^{\mathrm{2}}…

let-f-a-a-2-x-4-dx-1-determine-a-explicit-form-of-f-a-2-find-dx-a-2-x-4-a-gt-0-

Question Number 51988 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{f}\left({a}\right)\:=\int\:\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{4}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int\:\:\:\:\frac{{dx}}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{4}} }} \\ $$$${a}>\mathrm{0} \\ $$ Terms…

Question-117511

Question Number 117511 by Canovas last updated on 12/Oct/20 Answered by bemath last updated on 12/Oct/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\left(\mathrm{4}−\mathrm{9tan}\:^{\mathrm{2}} \mathrm{x}\right)}\:=\:\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{4}−\mathrm{9tan}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx} \\ $$$$=\:\int\:\frac{\mathrm{d}\left(\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{4}−\mathrm{9tan}\:^{\mathrm{2}} \mathrm{x}}\:=\:\int\:\frac{\mathrm{d}\varphi}{\mathrm{4}−\mathrm{9}\varphi^{\mathrm{2}} }…