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# Estimate the numerical value of $\displaystyle \int_0^\infty e^{-x^2}\ dx$ by writing it as the sum of $\displaystyle \int_0^4 e^{-x^2}\ dx$ and $\displaystyle \int_4^\infty e^{-x^2}\ dx$. Approximate the first integral by using Simpson's Rule with $n = 8$ and show that the second integral is smaller than $\displaystyle \int_4^\infty e^{-4x}\ dx$, which is less than 0.0000001.

## $\int_{0}^{\infty} e^{-x^{2}} d x \approx 0.886196$

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### Video Transcript

the problem is estimated. The numerical wild off improper, integral of two negative Black square from territory. Infinity writing me it as the sum of and you're from their four plus interior from four to infinity approximated the first integral by using Simpsons Rule was N is equal to eight. And show that the second interview is smaller. That into Europe from forty infinity to negative blacks, which is the last time your point there is a there is a chosen one, which is where a virus More. Now it's anti girl. From what? There to infinity to negative Black Square is Jax. This is equal to an integral from zero to war. You two make back square yaks us integral from forty infinitely. You too. Negative ax squared dx For this part they use Simpsons rule was and you go to aid. We can find it. Zez, this is called too. Zero point eight and six two. And now look at it Integral from forty infinity to negative back square. So axe is greeted at four on this and you're old, we have x square. It's illegal. Tow X, Hammes, axe access, insecurities and forces. This is reasons are all ex so negative act square. It's smaller than negative. Relax. So you two negative at square. It's smaller than each negative. Relax. So this integral a small Isa into girl from war to infinity. You too. Next to you. Oh, the box, Jax. Since this integral is why every where's Moore? So we can ask, I estimate and a girl from there to infinity to negative ax squared DX Is it just Teo? The first one's a zero point and it six two.

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