Prove that $\lim_{n\rightarrow \infty} \int_{[0,1]^n}\frac{|x|}{\sqrt{n}}=\frac{1}{\sqrt{3}}$
Prove that $$\lim_{n\rightarrow \infty} \int_{[0,1]^n}\frac{|x|}{\sqrt{n}}=\frac{1}{\sqrt{3}},$$
where $[0,1]^n=[0,1]\times \dots \times [0,1]$ is the unit cube in $\mathbb{R}^n$.
![Leopoldpilot](https://matchmaticians.com/storage/user/100022/thumb/matchmaticians-9kjdrv-file-1-avatar-512.jpg)
28
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
![Erdos](https://matchmaticians.com/storage/user/100028/thumb/matchmaticians-3empnt-file-5-avatar-512.jpg)
4.7K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 538 views
- $20.00
Related Questions
- Use Rouche’s Theorem to show that all roots of $z ^6 + (1 + i)z + 1 = 0$ lines inside the annulus $ \frac{1}{2} \leq |z| \leq \frac{5}{4}$
- Figuring out the maths for the probability of two adopted teens randomly being matched as pen pals in 2003
- Choosing the right statistical tests and how to organize the data accourdingly (student research project)
- Find the limit as x --> +inf
- Find slope intercept equation
- Does $\lim_{n \rightarrow \infty} \frac{2^{n^2}}{n!}$ exist?
- Computing mean, median, inter-quartile range, and standard deviation
- Determine the surface area of a ball, rotating a function about $x$-axis.