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Show that $ \displaystyle \int_0^\infty e^{-x^2}\ dx = \displaystyle \int_0^1 \sqrt{-\ln y}\ dy $ by interpreting the integrals as areas.

$\int_{0}^{\infty} e^{-x^{2}} d x=\int_{0}^{1} \sqrt{-\ln y} d y$

Integration Techniques

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