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Category: Integration

Question-163349

Question Number 163349 by smallEinstein last updated on 06/Jan/22 Answered by Ar Brandon last updated on 06/Jan/22 $${I}=\int_{−\infty} ^{\infty} \left(\int_{−\infty} ^{\infty} {e}^{−\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}\sqrt{\mathrm{2}}{xy}+\mathrm{3}{y}^{\mathrm{2}} \right)} {dx}\right){dy}…

1-findf-a-0-1-x-2-x-a-dx-with-a-gt-1-2-2-explicite-g-a-0-1-dx-x-2-x-a-3-calculate-0-1-dx-x-2-x-3-

Question Number 97800 by abdomathmax last updated on 09/Jun/20 $$\left.\mathrm{1}\right)\:\mathrm{findf}\left(\mathrm{a}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{a}}\mathrm{dx}\:\:\:\:\:\mathrm{with}\:\mathrm{a}>\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{a}}}\: \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}\:+\mathrm{3}}} \\ $$…

solve-y-y-1-cosx-

Question Number 97794 by abdomathmax last updated on 09/Jun/20 $$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{y}\:=\frac{\mathrm{1}}{\mathrm{cosx}} \\ $$ Commented by john santu last updated on 10/Jun/20 $$\mathrm{y}''+\mathrm{y}'\:=\:\mathrm{sec}\:\mathrm{x} \\ $$$$\mathrm{homogenous}\:\mathrm{solution}\: \\…