Question

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?

Answer 1

HOW IT IS ZERO??
I AM GETTING INFINITY.

Answer 2

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

\[\int\limits \limits_{-\infty}^{a} x^{3}dx+\int\limits \limits_{a}^{\infty} x^{3}dx\]

Answer 3

BUT STILL IT IS INFINITY NOT ZERO

Answer 4

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

Answer 5

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.