Is this statement true?

[cstvlr]

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

But as n approaches infinity the answer becomes zero.

 

[Char. Limit]

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.

 

[cstvlr]

Ok, thanks.

 

[Mute]

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.

 

[D H]

It is true as long as $n \geq 0$. For n < 0, it is not true.

Correction: It is true as long as n > -1, not zero.

 

[Mute]

Correction: It is true as long as n > -1, not zero.

Corrected. Thanks. I forgot to edit that when I decided not to talk only about integers.