# Is this statement true?

## Main Question or Discussion Point

int x^n from 0 to 1 = 1/(n + 1)

But as n approaches infinity the answer becomes zero.

Char. Limit
Gold Member
Yep. And if you look at x^n for some number 0<x<1 and 0<n, x^n will get smaller as n increases. It's only natural to see the integral get smaller as well.

Ok, thanks.

Mute
Homework Helper
int x^n from 0 to 1 = 1/(n + 1)

But as n approaches infinity the answer becomes zero.
It is true as long as $n > -1$. For n < 0, it is not true.

Last edited:
D H
Staff Emeritus
It is true as long as $n \geq 0$. For n < 0, it is not true.