Integral of e^-ax^2 from 0 to infinity - updated 💪

The integral of e^-x^2 from 0 infinity to infinity is sqrt(π/a)/2. This function is also expressed as e^(-x^2). This is a Gaussian function that is common in calculus, physics, and chemistry.
Here's a super-detailed version of this integral: • Integral of e^-x^2 fro...
I got tons of modifications of this type of integral. Check them out in my integrals playlist!
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[@jperez7893]

this is great stuff! i hope you can derive the physics of a pendulum without the typical derivation of sin theta ~ theta. in other words, the bessel functions of the first and second kinds and how to derive the constants

[@sayanmazumder2254]

Just substitute x^2=t. Differentiate and rearrange to get a form of Gamma function. Evaluate it by standard values. Simple.