# Integration

• Sep 3rd 2010, 08:39 AM
MAX09
Integration
Hi,

Is approximation the only way to solve Integral of e^(-x^2)/2 ?

What if the integral is indefinite? Any suggestions?

Thanks,
Max
• Sep 3rd 2010, 09:37 AM
wonderboy1953
I remember this integral being expressible in terms of pi.
• Sep 3rd 2010, 09:59 AM
HallsofIvy
The definite integral from 0 to infintity or from negative infinity to infinity is "expressible in terms of $\pi$".

Whether "approximation the only way" depends upon what you mean by "approximation".

$\int_0^x e^{-t^2} dt= Erf(x)$.

Would you consider $\int_0^x \frac{dt}{1+ t^2}= arctan(x)$ only done by "approximation"? If not, how would you find arctan(x) for general x?
• Sep 3rd 2010, 09:59 AM
AllanCuz
Quote:

Originally Posted by wonderboy1953
I remember this integral being expressible in terms of pi.

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 $\frac{ \sqrt{ \pi } }{2}$. 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