Integral of exp(-x^2) (HD Version)

Multivariable calculus: We calculate the integral of exp(-x^2) over the real line. This calculation involves a double integral, from which values are calculated using polar coordinates. Added: a numerical estimate, and an added tighter proof with the Squeeze Theorem.

Category:

Education

Tags:

• Mathematics
• multivariable
• calculus
• integral
• exponential
• Gaussian
• normal
• distribution
• polar
• coordinates
• harmonic
• oscillator

[newtonisaacma]

its very easy to prove it by gamma function

[MathDoctorBob]

@newtonisaacma Sure. But who develops the Gamma function in a multivariable calculus class? - Bob

[faisalabdulfattah]

It's crazy how useful this was. I was totally stuck at a similar problem, and this cleared it up entirely. Thank you.

[MathDoctorBob]

@faisalabdulfattah You're welcome! What problem were you working on? I'm always looking for good topics. - Bob

[faisalabdulfattah]

@MathDoctorBob I'll send you the link in a message, I can't post it here. It's pretty much the same problem you were doing, except it was for a specific region. The reason I was stuck was that I turned -x^2-y^2 into r^2, not -r^2. It's amazing how much of a difference that makes. Thanks again!

[MathDoctorBob]

@faisalabdulfattah Thanks for the link! A minus sign can definitely ruin your day. - Bob

[MathDoctorBob]

@candamohcine You're welcome! - Bob

[candamohcine]

Thank You Professor :)

[mathrock87]

integrate e^(-x^2-x^-2) how do ı fix:(