Question

HOw to integrate e^((-x^2)/2) ????

Answer 1

it has to be done with nummerical stuff i beleive

Answer 2

if we were to try to devise a function from which it came from wed have to have a \(exp(\frac{-x^2}{2})\) in it i believe

Answer 3

which means were are missing a -x from the equation to compensate for it

Answer 4

Amistre, can you take a look at my work here when you get a moment. I'm not sure if i got it write.

http://openstudy.com/#/updates/4eaac757e4b02eee39e329e4

Answer 5

There is no indefinite integral of that function in terms of elementary functions.

However if you are integrating that function from 0 to infinity--or -infinity to infinity--it can be done analytically without recourse to numerical methods.

Answer 6

analytic, thats the term i was trying to think of :)

Answer 7

But if you want
\[ \int_0^a \ e^{-x^2/2} \ dx \]
then you need numerical methods, or look it up in a table as it turns out this integral is quite well known and extremely important in statistics.

Answer 8

from 0 to 1

Answer 9

As I say, this can't be done analytically, but can be found from a table; in this case a table of Z values, where in this case the value of Z is 1.

Answer 10

As an indefinite integral, this is not expressible by elementary functions.As definite integral this function is very similar to Gaussian integral ( http://en.wikipedia.org/wiki/Gaussian_integral)

Answer 11

I think this could be done analytically see here : http://en.wikipedia.org/wiki/Integral_of_a_Gaussian_function

Answer 12

but I may be wrong ..!! I will try myself and get back to you .. :)

Answer 13

Thank you!

Answer 14

Glad to help :)