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

  • Thread starter cstvlr
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In summary, the integral of x^n from 0 to 1 is equal to 1/(n+1), but as n approaches infinity, the answer becomes zero. This is only true for n > -1 and the integral gets smaller as n increases.
  • #1
cstvlr
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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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  • #2
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.
 
  • #3
Ok, thanks.
 
  • #4
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 [itex]n > -1[/itex]. For n < 0, it is not true.
 
Last edited:
  • #5
Mute said:
It is true as long as [itex]n \geq 0[/itex]. For n < 0, it is not true.
Correction: It is true as long as n > -1, not zero.
 
  • #6
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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