Intuitively, $$\int\limits \limits_{-\infty}^{\infty} x^{3}dx$$ should be 0 because it is an odd function, but apparently it diverges. Can anyone give me an intuitive explanation why?

Question

anonymous · Answer

HOW IT IS ZERO??
I AM GETTING INFINITY.

zarkon · Answer

in order for $$\int\limits \limits_{-\infty}^{\infty} x^{3}dx$$ to converge the folowwing have to each converge

$$\int\limits \limits_{-\infty}^{a} x^{3}dx+\int\limits \limits_{a}^{\infty} x^{3}dx$$

anonymous · Answer

BUT STILL IT IS INFINITY NOT ZERO

zarkon · Answer

it is not infinity...the integral does not converge

zarkon · Answer

alexray19, I believe, is under the false impression that 

$$\int\limits \limits_{-\infty}^{\infty} x^{3}dx$$

is the same as 

$$\lim_{a\to\infty}\int\limits \limits_{-a}^{a} x^{3}dx$$

which it is not.