Hi,
Is approximation the only way to solve Integral of e^(-x^2)/2 ?
What if the integral is indefinite? Any suggestions?
Thanks,
Max
The definite integral from 0 to infintity or from negative infinity to infinity is "expressible in terms of $\displaystyle \pi$".
Whether "approximation the only way" depends upon what you mean by "approximation".
$\displaystyle \int_0^x e^{-t^2} dt= Erf(x)$.
Would you consider $\displaystyle \int_0^x \frac{dt}{1+ t^2}= arctan(x)$ only done by "approximation"? If not, how would you find arctan(x) for general x?
You're thinking of the Gaussian integral: Gaussian integral - Wikipedia, the free encyclopedia
To answer the OP, if the bounds are from negative infinity to infinity then the integral will become $\displaystyle \frac{ \sqrt{ \pi } }{2} $. If, however, the bounds are finite the integral cannot be expressed in elementary functions: http://integrals.wolfram.com/index.jsp?expr=e^(-x^2)&random=false