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Category: Integration

p-5-6-p-p-8-11-p-11-13-12ky-x-2-6x-dx-p-4-7-p-p-9-12-p-11-16-x-2-y-3-2-k-dx-solve-for-y-

Question Number 105239 by bemath last updated on 27/Jul/20 $$\underset{\underset{{p}=\mathrm{5}} {\overset{\mathrm{6}} {\sum}}{p}} {\overset{\underset{{p}=\mathrm{8}} {\overset{\mathrm{11}} {\sum}}{p}} {\sum}}\:\underset{\mathrm{11}} {\overset{\mathrm{13}} {\int}}\left(\frac{\mathrm{12}{ky}}{{x}^{\mathrm{2}} }\:+\:\mathrm{6}{x}\right)\:{dx}\:=\:\underset{\underset{{p}=\mathrm{4}} {\overset{\mathrm{7}} {\sum}}{p}} {\overset{\underset{{p}=\mathrm{9}} {\overset{\mathrm{12}} {\sum}}{p}} {\sum}}\:\underset{\mathrm{11}}…

let-S-n-0-n-x-1-x-x-1-x-3-dx-1-calculate-S-n-2-find-lim-n-S-n-

Question Number 39660 by abdo mathsup 649 cc last updated on 09/Jul/18 $${let}\:\:{S}_{{n}} \:\:=\:\int_{\mathrm{0}} ^{{n}} \:\:\:\:\:\frac{{x}\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\left({x}+\mathrm{1}\:−\left[{x}\right]\right)^{\mathrm{3}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{S}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:{S}_{{n}} \\ $$…

Question-170725

Question Number 170725 by Sotoberry last updated on 29/May/22 Answered by FelipeLz last updated on 30/May/22 $${u}\:=\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:\Rightarrow\:{du}\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$${dv}\:=\:\mathrm{1}{dx}\:\Rightarrow\:{v}\:=\:{x} \\ $$$$\int\mathrm{tan}^{−\mathrm{1}} \left({x}\right){dx} \\…