Title: ETH_Sem4 / Advanced_Kinetics / Important_Integrals

Q: \[\int dx e^{-\alpha x^2} =[...]\]
A: \sqrt{\frac{\pi}{\alpha} }

Q: \[\int_0^\infty dx~x e^{-a x^2} = [...]\]
A: \frac{1}{2a}

Q: \[\int dx x^2 e^{-a x^2} = [...]\]
A: \sqrt\frac{\pi}{4a^3}

Q: \[\int dx x e^{-a x^2} = [...]\]
A: 0