Is the statement 'int x^n from 0 to 1 = 1/(n + 1)' true?

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SUMMARY

The statement 'int x^n from 0 to 1 = 1/(n + 1)' is true for n > -1 and false for n < 0. As n approaches infinity, the integral approaches zero, particularly for values of x where 0 < x < 1. The integral decreases as n increases, confirming the behavior of the function. This conclusion is critical for understanding the limits of integration in calculus.

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

But as n approaches infinity the answer becomes zero.
 
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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.
 
cstvlr said:
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 &gt; -1. For n < 0, it is not true.
 
Last edited:
Mute said:
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.
 
D H said:
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.
 

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