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Category: Integration

1-find-f-a-0-1-dx-ax-1-x-2-x-1-with-a-gt-0-2-calculate-f-a-3-find-the-value-of-0-1-xdx-ax-1-2-x-2-x-1-4-calculate-0-1-dx-2x-1-x-2-x-1-

Question Number 53228 by maxmathsup by imad last updated on 19/Jan/19 $$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\left({ax}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}}\:\:\:{with}\:\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({a}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\left({ax}+\mathrm{1}\right)^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}} \\…

Let-f-x-2x-x-2-4-a-Find-b-b-f-x-dx-for-b-gt-0-b-Determine-f-x-dx-is-convergent-or-not-

Question Number 53212 by Joel578 last updated on 19/Jan/19 $$\mathrm{Let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} \:+\:\mathrm{4}} \\ $$$$ \\ $$$$\left({a}\right)\:\mathrm{Find}\:\underset{−{b}} {\overset{{b}} {\int}}\:{f}\left({x}\right)\:{dx},\:\mathrm{for}\:{b}\:>\:\mathrm{0} \\ $$$$\left({b}\right)\:\mathrm{Determine}\:\underset{−\infty} {\overset{\infty} {\int}}\:{f}\left({x}\right)\:{dx}\:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\:\mathrm{not} \\ $$ Commented by…

Question-118710

Question Number 118710 by eric last updated on 19/Oct/20 Answered by mathmax by abdo last updated on 19/Oct/20 $$\mathrm{M}=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\mathrm{dx}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{lnx}}{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\mathrm{dx}\:+\int_{\mathrm{1}}…

Question-118679

Question Number 118679 by Algoritm last updated on 19/Oct/20 Answered by 1549442205PVT last updated on 19/Oct/20 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left[\mathrm{2x}\right].\mathrm{x}}{\left[\mathrm{2x}\right]+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}=\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\left[\mathrm{2x}\right].\mathrm{x}}{\left[\mathrm{2x}\right]+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}+\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \frac{\left[\mathrm{2x}\right].\mathrm{x}}{\left[\mathrm{2x}\right]+\mathrm{x}^{\mathrm{2}}…

x-sin-x-1-cos-2-x-dx-

Question Number 118668 by bemath last updated on 19/Oct/20 $$\:\:\int\:\frac{{x}\mid\mathrm{sin}\:{x}\mid}{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\:? \\ $$ Answered by Lordose last updated on 19/Oct/20 $$\Omega=\int\:\frac{\mathrm{x}\mid\mathrm{sinx}\mid}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$$$\Omega=\int\mathrm{x}\mid\mathrm{cosecx}\mid\mathrm{dx}\: \\…