I don't know how to derive this (my red pen mark)
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Have you tried expanding the integrand in Taylor series? – saulspatz Dec 28 '20 at 18:51
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Do you mean take the derivative by derive, or solve the integral? I am a bit confused... To solve the integral, see here: https://math.stackexchange.com/questions/502313/what-is-the-integral-of-e-x2-2-over-mathbbr – TheBestMagician Dec 28 '20 at 18:51
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Possible explanation:
Since $\left| -\frac{1}{\sqrt n} \right | \approx 0,$ the interval of integration is very close to zero, and so $x^2 \approx 0 \implies e^{-x^2/2} \approx 1$.
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When $x \approx 0$, we have $e^{-x^2/2} \approx 1$. Since the text states that we are doing a slightly less than rigorous proof, replace $e^{x^2/2}$ with $1$ and the answer follows immediately.
