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find-lim-0-0-pi-2-dx-sin-2-x-cos-2-x-




Question Number 28680 by abdo imad last updated on 28/Jan/18
find  lim_(ξ→0)    ∫_0 ^(π/2)      (dx/( (√(sin^2 x +ξcos^2 x))))     .
$${find}\:\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{dx}}{\:\sqrt{{sin}^{\mathrm{2}} {x}\:+\xi{cos}^{\mathrm{2}} {x}}}\:\:\:\:\:. \\ $$

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