Question

What is the integral of e^(x^2)

Answer 1

it is provable you cannot express that integral with "elementary" functions, in statistics they give the integral of e^-(x^2) as erf(x) , and im pretty sure \[\int\limits_{?}^{?} e^{x^2} = 0.5\sqrt{\pi }erfi(x)\]

Answer 2

aahh i forgot the values on the integral..

Answer 3

But Im talking about an indefinite integral

Answer 4

yes, i was going to have the lower limit as x1 and the upper as x2 ( i prefer definite) but its the same problem effectively

Answer 5

I didn't get you.Please elaborate

Answer 6

most functions we come across can be integrated, but this function cannot, because you can show that nothing differentiates to make that function. its similar to this: http://en.wikipedia.org/wiki/Gaussian_integral

Answer 7

the area under the curve exists, but we cannot express it in terms of any elementary functions

Answer 8

using polar coordinates i think it is possible to compute the integral i think, although im not sure how much of polar coordinates you have come across, you should take a look its really interesting

Answer 9

Yeah I guess we are still not as advanced in integration as in differentiation as we don't have a solid definition for integration like we have for differentiation

Answer 10

And yeah I have some basic insights into polar coordinates.It's pretty interesting