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Category: Integration

sin-8-x-cos-8-x-1-2sin-2-x-cos-2-x-a-1-2-sin-2x-b-1-2-sin-2x-c-None-

Question Number 49746 by rahul 19 last updated on 10/Dec/18 $$\int\frac{\mathrm{sin}^{\mathrm{8}} {x}−\mathrm{cos}^{\mathrm{8}} {x}}{\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} {x}.\mathrm{cos}^{\mathrm{2}} {x}}\:=\:? \\ $$$$\left.{a}\left.\right)\left.\:\frac{−\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{x}\:\:\:{b}\right)\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{x}\:\:\:{c}\right){None}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…

If-f-x-is-a-differentiable-function-defined-x-R-such-that-f-x-3-x-f-x-0-then-0-2-f-1-x-dx-

Question Number 115267 by bobhans last updated on 24/Sep/20 $${If}\:{f}\left({x}\right)\:{is}\:{a}\:{differentiable}\:{function} \\ $$$${defined}\:\:\forall{x}\in\mathbb{R}\:{such}\:{that}\:\left({f}\left({x}\right)\right)^{\mathrm{3}} −{x}+{f}\left({x}\right)=\mathrm{0} \\ $$$${then}\:\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{2}}} {\int}}\:{f}^{−\mathrm{1}} \left({x}\right)\:{dx}\:=\: \\ $$ Answered by Olaf last updated…

advanced-mathematics-digamma-limit-if-k-gt-0-then-prove-that-lim-x-0-1-x-k-

Question Number 115193 by mnjuly1970 last updated on 24/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{mathematics}…\:\: \\ $$$$\:\:\:\:\:\:\:::\:\:\:{digamma}\:\:{limit}\:\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:{if}\:\:\:{k}>\mathrm{0}\:\:{then} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{1}}{{x}}\left(\psi\left(\frac{{k}+{x}}{\mathrm{2}{x}}\right)\:−\:\psi\left(\frac{{k}}{\mathrm{2}{x}}\right)\right)\:=\frac{\mathrm{1}}{{k}}\:\:\:\:\checkmark \\ $$$$ \\ $$$$\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970}……

calculate-D-x-2-y-2-x-2-y-2-dxdy-with-D-x-y-R-2-1-x-1-and-0-y-2-

Question Number 49646 by maxmathsup by imad last updated on 08/Dec/18 $${calculate}\:\int\int_{{D}} \left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy}\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{0}\leqslant{y}\leqslant\mathrm{2}\:\right\} \\ $$ Terms of Service…