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Category: Integration

Question-125876

Question Number 125876 by bramlexs22 last updated on 14/Dec/20 Commented by liberty last updated on 15/Dec/20 $${W}\:=\:\underset{{n}\rightarrow\infty} {\mathrm{Lim}}\:\underset{{i}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\rho{A}\left({x}_{{i}} ^{\ast} \right)\Delta{x}\:\:\:\:\:\:\: \\ $$$${W}\:=\:\underset{{n}\rightarrow\infty} {\mathrm{Lim}}\:\underset{{i}\:=\:\mathrm{1}}…

Question-60320

Question Number 60320 by Sardor2211 last updated on 19/May/19 Commented by maxmathsup by imad last updated on 20/May/19 $${let}\:{I}\:=\int\:\:\frac{{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} \:+\mathrm{5}{x}\:+\mathrm{23}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−\mathrm{5}\right)}{dx}\:\:{let}\:{decompose}\:{F}\left({x}\right)\:=\frac{{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} \:+\mathrm{5}{x}\:+\mathrm{23}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−\mathrm{5}\right)}…

Question-60318

Question Number 60318 by Sardor2211 last updated on 19/May/19 Commented by kaivan.ahmadi last updated on 20/May/19 $${we}\:{find}\:{I}=\int{x}^{\mathrm{2}} {arctgx}\:{dx}\:{then}\:{multiply}\:\mathrm{4} \\ $$$${u}={arctgx}\Rightarrow{du}=\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$${dv}={x}^{\mathrm{2}} {dx}\Rightarrow{v}=\frac{{x}^{\mathrm{3}} }{\mathrm{3}}…

Given-f-x-f-x-2-x-R-if-0-2-f-x-dx-k-then-0-1010-f-x-2a-dx-for-a-Z-

Question Number 125841 by bramlexs22 last updated on 14/Dec/20 $${Given}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right)\:\forall{x}\in\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{f}\left({x}\right){dx}={k}\:{then}\:\underset{\mathrm{0}} {\overset{\mathrm{1010}} {\int}}{f}\left({x}+\mathrm{2}{a}\right){dx}\:? \\ $$$${for}\:{a}\in\mathbb{Z}\: \\ $$ Commented by mr W last…