Question

Is my result for the following integral corect or did I make a mistake? \[\int e ^{-x^{2}}dx\] My result was \[-e^{-2x}/2 + C\]

Answer 1

http://www.wolframalpha.com/input/?i=int%28e%5E%28-x%5E2%29%29dx

Answer 2

I already tried that , erf(x) isn't an accepted result by most teachers :P

Answer 3

well at least no my teacher :(

Answer 4

yeah, you are right
but actually, yours still incorrect :P
im not sure anyone can solve this

Answer 5

no, i cant..
it is so hard :)

Answer 6

There is no anti-derivative (in terms of elementary functions) for \[e^{-x^2}.\]Whoever gave that to you to solve is playing a cruel joke. If the problem were:\[\int\limits xe^{-x^2}dx\]that would be a different story.

Answer 7

The best you can hope for (as far as an anti-derivative you can see) is an infinite power series, but most dont except that as an answer.

Answer 8

thank you

Answer 9

welcome, heh :)

Answer 10

http://www.physicsforums.com/showthread.php?t=127015

Answer 11

The hard reality of integration is that even after you learn all the different techniques (integration by parts, u-sub, trig-sub, partial fractions, etc), many many many integration problems cannot be solved by hand.

Answer 12

Maybe it was something like this:\[\int\limits x^3e^xdx\]That can be solved by parts.

Answer 13

ok, you convinced me that it cannot be solved. I give up.

Answer 14

@SithsAndGiggles

Answer 15

If this were a definite integral, such as over the interval \([0,\infty)\), you could consider
\[\left(\int_0^\infty e^{x^2}~dx\right)^2\]
then write that as the product of two integrals. Change the variable of one, and you can combine the integrals into a double integral, which you could then work with by converting to polar coordinates.

But if this is indeed an indefinite integral... no luck.

Answer 16

ok, got it. I'll be back. thank you

Answer 17

hey friend, you said that you don't know whether the answer is correct or not, I asked my professor about your question, you can trust him since he is a Ph.D in math department in my college and he is willing to answer any of my questions. I am sorry for my ambiguous question lead to his answer without solution, but if you want, I can ask him for that. Here what he said:
Dear Professor,
This is Hoa. Please, help me with this
Can we take integral of e^(-x^2) dx?
Thanks in advance
You can, because it is continuous and any continuous function can be integrated. You get a function which is more or less the Gaussian probability distribution function. It cannot be expressed in terms of "elementary functions" -- some people will say "you can't integrate it" but they really mean "there is no elementary antiderivative".

Reid Huntsinger

Answer 18

Thanks a lot for your help, after your message I searched the Gaussian probability distribution on google and found this http://en.wikipedia.org/wiki/Gaussian_integral , it solves this exact problem in a few different ways.

Answer 19

that is what SithAndGiggles talked above, isn't it? you bad, me bad!!!ask for help and didn't trust the helper!! have to say sorry to him. "I am sorry, SithAndGiggles""