http://www.webassign.net/cgi-bin/sym...%20dx%20%3D%20
I know this improper integral converges, but now I don't know how to work it out and find the limit...
Any help will be appreciated!
http://www.webassign.net/cgi-bin/sym...%20dx%20%3D%20
I know this improper integral converges, but now I don't know how to work it out and find the limit...
Any help will be appreciated!
Have you ever heard of the gamma distribution? It can be shown that...
$\displaystyle \int_0^{\infty} x^a e^{-bx} dx= \frac{\Gamma (a+1)}{b^{a+1}} = \frac{a!}{b^{a+1}}$
$\displaystyle \int_0^{\infty} x^1 e^{-5.9x} dx= \frac{\Gamma (2)}{(5.9)^{2}} = \frac{1!}{(5.9)^{2}}$