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Category: Integration

calculate-D-e-x-2-y-2-x-2-y-2-z-2-dxdydz-with-D-x-y-z-R-3-0-x-1-1-y-2-and-2-z-3-

Question Number 62213 by maxmathsup by imad last updated on 17/Jun/19 $${calculate}\:\int\int\int_{{D}} \:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} }{dxdydz}\:{with} \\ $$$${D}\:=\left\{\left({x},{y},{z}\right)\in{R}^{\mathrm{3}} \:/\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}\:\:{and}\:\:\:\mathrm{2}\leqslant{z}\leqslant\mathrm{3}\:\right\} \\ $$ Commented…

calculate-x-3-x-2-x-2-x-1-dx-

Question Number 62207 by maxmathsup by imad last updated on 17/Jun/19 $${calculate}\:\int\:\:\:\:\:\:\frac{{x}+\mathrm{3}}{\left({x}−\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 18/Jun/19 $${I}\:=\int\:\frac{{x}−\mathrm{2}\:+\mathrm{5}}{\left({x}−\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}}…

calculate-W-e-x-2y-sin-x-2y-dxdy-W-x-y-2-0-x-1-and-2-y-5-

Question Number 62201 by maxmathsup by imad last updated on 17/Jun/19 $${calculate}\:\int\int_{{W}} \:\:{e}^{{x}−\mathrm{2}{y}} {sin}\left({x}+\mathrm{2}{y}\right)\:{dxdy} \\ $$$${W}\:=\left\{\left({x},{y}\right)^{\mathrm{2}} /\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:\:{and}\:\:\mathrm{2}\leqslant{y}\leqslant\sqrt{\mathrm{5}}\right\} \\ $$ Commented by mathmax by abdo last…