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Category: Integration

Integrate-the-function-f-x-y-xy-x-2-y-2-over-the-domain-R-3-x-2-y-2-3-1-xy-4-

Question Number 98520 by bobhans last updated on 14/Jun/20 $$\mathrm{Integrate}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{xy}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right) \\ $$$$\mathrm{over}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{R}:\left\{−\mathrm{3}\leqslant\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \leqslant\mathrm{3},\:\mathrm{1}\leqslant\mathrm{xy}\leqslant\mathrm{4}\right\} \\ $$ Answered by john santu last updated on…

Question-32958

Question Number 32958 by artibunja last updated on 07/Apr/18 Commented by MJS last updated on 07/Apr/18 $$\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{10}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}}+\frac{\left(−\mathrm{3}+\frac{\mathrm{5}}{\mathrm{3}}\right){x}+\left(−\mathrm{10}−\frac{\mathrm{2}}{\mathrm{3}}\right)}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{4}}{\mathrm{3}}×\frac{{x}+\mathrm{8}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}} \\ $$$$\mathrm{3}{x}^{\mathrm{2}}…

1-study-the-convergence-of-0-1-x-p-1-x-dx-2-find-lim-p-0-1-x-p-1-x-dx-

Question Number 32939 by abdo imad last updated on 06/Apr/18 $$\left.\mathrm{1}\right)\:{study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{{p}} }{\mathrm{1}+{x}}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{p}\rightarrow\infty} \:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{{p}} }{\mathrm{1}+{x}}{dx}\:. \\ $$ Commented by abdo…

Question-98463

Question Number 98463 by pranesh last updated on 14/Jun/20 Answered by maths mind last updated on 15/Jun/20 $$\underset{{k}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\frac{{x}^{{k}} }{{k}}=\int\frac{\mathrm{1}−{x}^{\mathrm{99}} }{\mathrm{1}−{x}}{dx} \\ $$$$\left({cot}\left({x}\right)+……+\frac{{cot}^{\mathrm{99}} \left({x}\right)}{\mathrm{99}}\right)+\int\left(\mathrm{1}+{cot}\left({x}\right)\right)\left(\mathrm{1}+{cot}^{\mathrm{99}}…

let-f-x-x-2-2pi-periodi-even-developp-f-at-fourier-serie-

Question Number 98428 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} \:\:,\mathrm{2}\pi\:\mathrm{periodi}\:\mathrm{even}\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{f}\:\mathrm{is}\:\mathrm{even}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{a}_{\mathrm{0}}…