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Category: Integration

let-f-x-y-x-y-x-y-1-calculate-D-f-x-y-dxdy-with-D-x-y-R-2-1-x-2-and-1-y-3-

Question Number 65401 by mathmax by abdo last updated on 29/Jul/19 $${let}\:{f}\left({x},{y}\right)=\left({x}+{y}\right)\sqrt{{x}+{y}−\mathrm{1}} \\ $$$${calculate}\:\:\int\int_{{D}} {f}\left({x},{y}\right){dxdy}\:{with}\: \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:\:{and}\:\:\:\mathrm{1}\leqslant{y}\leqslant\sqrt{\mathrm{3}}\right\} \\ $$ Commented by mathmax by abdo…

1-calculate-A-n-1-n-2-sin-x-2-3y-2-e-x-2-3y-2-dxdy-2-determine-lim-n-A-n-

Question Number 65398 by mathmax by abdo last updated on 29/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:\:{A}_{{n}} =\int\int_{\left[\mathrm{1},{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\:\:{sin}\left({x}^{\mathrm{2}} \:+\mathrm{3}{y}^{\mathrm{2}} \right)\:{e}^{−{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} } {dxdy} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$…

Question-65395

Question Number 65395 by imron876 last updated on 29/Jul/19 Commented by mathmax by abdo last updated on 29/Jul/19 $$\int\:\left(−\mathrm{1}\right)^{{x}} {dx}\:=\int\:{e}^{{i}\pi{x}} {dx}\:=\frac{\mathrm{1}}{{i}\pi}{e}^{{i}\pi{x}} \:+{c}\:=\frac{\left(−\mathrm{1}\right)^{{x}} }{{i}\pi}\:+{c} \\ $$…

I-1-e-dx-x-1-ln-2-x-

Question Number 65372 by aliesam last updated on 29/Jul/19 $${I}=\int_{\mathrm{1}} ^{{e}} \:\frac{{dx}}{{x}\left(\mathrm{1}+{ln}^{\mathrm{2}} {x}\right)} \\ $$ Commented by Prithwish sen last updated on 29/Jul/19 $$\mathrm{put}\:\mathrm{lnx}=\mathrm{tan}\theta\Rightarrow\frac{\mathrm{dx}}{\mathrm{x}}=\mathrm{sec}^{\mathrm{2}} \theta\mathrm{d}\theta…

find-dx-x-1-x-2-x-3-

Question Number 65355 by mathmax by abdo last updated on 28/Jul/19 $${find}\:\int\:\:\:\frac{{dx}}{\:\sqrt{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)}} \\ $$ Commented by Prithwish sen last updated on 29/Jul/19 $$\int\frac{\mathrm{dx}}{\:\sqrt{\left\{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{1}\right\}\left(\mathrm{x}+\mathrm{2}\right)}}\:\:\:\mathrm{putting}\:\left(\mathrm{x}+\mathrm{2}\right)=\mathrm{a} \\…