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Category: Integration

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…

nice-calculus-evaluate-0-pi-2-0-pi-2-ln-cos-x-2-ln-cos-y-2-cos-x-cos-y-dxdy-

Question Number 127726 by mnjuly1970 last updated on 01/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:{evaluate}:: \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\left(\frac{{ln}\left({cos}\left(\frac{{x}}{\mathrm{2}}\right)\right)−{ln}\left({cos}\left(\frac{{y}}{\mathrm{2}}\right)\right)}{{cos}\left({x}\right)−{cos}\left({y}\right)}\right){dxdy} \\ $$$$ \\ $$ Terms of Service…

advanced-mathematics-prove-that-n-0-1-2-n-3n-n-3-125-11pi-6-2log-2-45-

Question Number 127725 by mnjuly1970 last updated on 01/Jan/21 $$\:\:\:\:\:\:\:…\:{advanced}\:\:{mathematics}… \\ $$$$\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}^{{n}} \begin{pmatrix}{\mathrm{3}{n}}\\{\:\:{n}}\end{pmatrix}}\:\overset{???} {=}\frac{\mathrm{3}}{\mathrm{125}}\left(\frac{\mathrm{11}\pi}{\mathrm{6}}−\mathrm{2}{log}\left(\mathrm{2}\right)+\mathrm{45}\right) \\ $$$$ \\ $$ Answered by Ar…

dx-sin3x-sin4x-

Question Number 62185 by aliesam last updated on 17/Jun/19 $$\int\frac{{dx}}{{sin}\mathrm{3}{x}+{sin}\mathrm{4}{x}} \\ $$ Answered by MJS last updated on 17/Jun/19 $$\int\frac{{dx}}{\mathrm{sin}\:\mathrm{3}{x}\:+\mathrm{sin}\:\mathrm{4}{x}}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\mathrm{1}}{\mathrm{cos}\:{x}}\:\rightarrow\:{dx}=\frac{\mathrm{cos}^{\mathrm{2}} \:{x}}{\mathrm{sin}\:{x}}\right] \\ $$$$=−\int\frac{{t}^{\mathrm{3}}…