I'm struggling to find this:
(integral) e^(-x^2)dx
Thanks for any help
I'm struggling to find this:
(integral) e^(-x^2)dx
Thanks for any help
why don't you look it up using google?
http://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions
Yes you can look it up online, but if you have not seen one like this before it is useful to know that you will not find a closed form answer in terms of usual functions.
square it- you get e^(-x^2)*e^(-x^2)
now change change it to
e^-(x^2+y^2)dxdy
just renaming variables
change to polar coordinates using r^2=x^2+y^2, dxdy=rdrd(theta)
Then you have r*e^(-r^2)drd(theta)
you then get -1/2*e^(-r^2)*theta and now you have to take the square root to get the right integral
you have to use this for a definite integral say from -infinity to infinity, or for 0 to infinity, and then you get root pi or root pi over 2.
wizzi wrote:
you have to use this for a definite integral say from -infinity to infinity, or for 0 to infinity, and then you get root pi or root pi over 2.
That seems a little more complicated than it needed to be, but maybe I don't know what I'm doing.
not smart wrote:
I'm struggling to find this:
(integral) e^(-x^2)dx
Thanks for any help
That integral is famous. You can't express the answer in terms of algebraic functions (sine, cosine, exponentials, polynomials) -- only an infinite polynomial (a power series). You can, however, write down a numerical solution if you have limits of integration, and you can do it with pen and paper if your limits of integration are either -inf to inf, or 0 to inf, or -inf to 0. To integrate from -inf to inf, you need to use the change of variables trick given above. Then you can use symmetry to get the integral from 0 to inf.
I wouldn't have said anything except it's really rotten for a teacher to give you that problem -- it's extremely hard to figure out the trick for yourself unless you've already seen it once. Are you sure you didn't have a different function?
agdfd wrote:
not smart wrote:I'm struggling to find this:
(integral) e^(-x^2)dx
Thanks for any help
I wouldn't have said anything except it's really rotten for a teacher to give you that problem -- it's extremely hard to figure out the trick for yourself unless you've already seen it once. Are you sure you didn't have a different function?
Agreed. This is not a standard BC Calc problem.