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

  • Thread starter Thread starter cstvlr
  • Start date Start date
Click For Summary
The statement "int x^n from 0 to 1 = 1/(n + 1)" is true for n greater than -1. As n approaches infinity, the integral approaches zero, reflecting that x^n diminishes for values of 0 < x < 1. For n less than 0, the statement does not hold true. The discussion emphasizes the importance of n's value in determining the validity of the integral. Overall, the integral's behavior is consistent with the properties of exponential decay as n increases.
cstvlr
Messages
12
Reaction score
0
int x^n from 0 to 1 = 1/(n + 1)

But as n approaches infinity the answer becomes zero.
 
Physics news on Phys.org
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.
 

Similar threads

Undergrad Infinite Series - Divergence of 1/n question
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Find ##\int_0^π \sin^ n x dx ##
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Is the functional derivative a function or a functional
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Solving the Difficult Integral ##\int_0^{\infty} x^{n+1} e^{-x} \sin(ax) dx##
  • · Replies 5 ·
Replies
5
Views
3K
High School Difficulty with understanding whether 1/n converges or diverges
  • · Replies 11 ·
Replies
11
Views
5K
Undergrad Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Integrating x^ne^xn: Analyzing & Solving
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Understanding Theorem 13 from Calculus 7th ed, R. Adams, C. Essex, 4.10
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Proof of 1/(x^2) Not Having Limit at 0
  • · Replies 5 ·
Replies
5
Views
2K
MHB Can the Series Sum Be Expressed as an Integral as N Approaches Infinity?
  • · Replies 3 ·
Replies
3
Views
2K