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Category: Integration

let-f-0-1-x-x-2-x-dx-with-gt-1-4-1-explicit-f-2-calculate-g-0-1-xdx-x-2-x-3-find-the-value-of-intehrals-0-1-x-x-2-x-2-dx-snd-0-1-xdx-

Question Number 92082 by mathmax by abdo last updated on 04/May/20 $${let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {x}\sqrt{{x}^{\mathrm{2}} −{x}+\alpha}{dx}\:\:\:\:\:\:{with}\:\alpha>\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\left.\mathrm{1}\right)\:{explicit}\:\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{xdx}}{\:\sqrt{{x}^{\mathrm{2}} −{x}+\alpha}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:{intehrals}\:\int_{\mathrm{0}} ^{\mathrm{1}}…

0-xsinx-1-cos-2-x-dx-

Question Number 26507 by yesaditya22@gmail.com last updated on 26/Dec/17 $$\overset{\Pi} {\int}_{\mathrm{0}} \frac{\mathrm{xsinx}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$ Answered by kaivan.ahmadi last updated on 26/Dec/17 $$\mathrm{I}=\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{xsinx}}{\mathrm{2}−\mathrm{sin}^{\mathrm{2}}…

1-1-xdx-x-2-1-2-

Question Number 26486 by A1B1C1D1 last updated on 26/Dec/17 $$\int_{\:−\mathrm{1}} ^{\:\:\mathrm{1}} \frac{\mathrm{xdx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by kaivan.ahmadi last updated on 26/Dec/17 $$\mathrm{u}=\mathrm{x}^{\mathrm{2}} +\mathrm{1}\Rightarrow\mathrm{du}=\mathrm{2xdx}…

arcsinx-2-dx-

Question Number 91996 by student work last updated on 04/May/20 $$\int\left(\mathrm{arcsinx}\right)^{\mathrm{2}} \mathrm{dx}=? \\ $$ Commented by jagoll last updated on 04/May/20 $$\mathrm{let}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=\:\mathrm{t}\: \\ $$$$\mathrm{x}\:=\:\mathrm{sin}\:\mathrm{t}\:\Rightarrow\mathrm{dx}\:=\:\mathrm{cos}\:\mathrm{t}\:\mathrm{dt}\:…