Question

Improper Integral:

Answer 1

\[\int\limits_{-\infty}^{\infty}x^5e ^{-x ^{6}}dx\]

Answer 2

Try checking to see you integrand has this property for an easy result: \(f(-x)=-f(x)\) ;)

Answer 3

I have no idea how to do it :/

Answer 4

Recall that if \(f\) is an odd function, then \(f(-x)=-f(x)\)

And for odd functions, you have that \[ \int_{-a}^af(x)\,dx=0\] for \(a>0\)

Answer 5

makes sense now ;) thanks

Answer 6

awesome =]