How Gauss solved the integral of e^(-x^2) from 0 to infinity

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[Ninja]

Very cool integral. Seeing this helps me to understand why the function for the normal distribution curve has the 1/sqrt(2*pi) in the front.

[breakoff]

I am obsessed with this integral and the gamma function

[Jacobiano_]

Can't believe a semester ago I mastered this and now I completely forgot how to solve this. Thanks for showing me I have to practice more.

[johns.]

I find it interesting that the jacobian matrix you end up getting is just the rotation matrix in R2 multiplied on the right by the column vector [1 ; r]. There must be an explicit reason for this beyond "the math just works out that way."

[HoldensBro]

The fact that he put this in calculus basics channel 😭

[FEg-xwjq]

I neeb to know the reson why the two therm integral combine togethe?

[JoseEliasOD]

Can you explain what the jacobian is and prove the formula to calculate it?

[李汶灏]

The region of this double integral is a circle, the bound for theta should be integrating from 0 to 2 pi, isn’t?

[sayanmazumder]

Sir this integral came in MAKAUT (West Bengal, India) examination in the year 2023. THe only problem is, we do not have this evaluation in our syllabus for BTech First semester. How do preliminary students have to solve ths integral. Please help

[shyamsundarsinha]

Is dx dy same as dy dx in I^2 function?

[Natnatcha]

how did u know that it is in the first quadrant?

[zachansen]

I think you posted this on the wrong channel -- this one says "calc basics"

[Sofia]

Normally the Gaussian integral equal to square root of pi from-♾ to ♾ it’s that okey

[李汶灏]

Why integrate theda from 0 to pi/2 but not 2pi?

[FEg-xwjq]

Sir, I don't understand the point of intigral multiplication? Plese shwo me

[tabridgazco.]

That is not correct manner, because the y= e^-x^2 is not equal the e^-y^2