All Questions
2
questions
3
votes
0
answers
64
views
Does this ridiculous integral converge?
I was looking through some of my older questions, when I came across this crazy integral I posted.
$\int\limits^{2}_{1}\sqrt{x-\sqrt{x!-\sqrt{(x!)!-\sqrt{((x!)!)!-\dots}}}}dx$
I had approximated it at ...
- 1,688
10
votes
1
answer
277
views
Evaluate: $\int_0^1 \sqrt{x+\sqrt{x^2+\sqrt{x^3+\cdots}}}\, dx. $
Is there a way to evaluate the integral:$$\int_0^1\sqrt{x+\sqrt{x^2+\sqrt{x^3+\sqrt{x^4+\cdots}}}}\,dx,$$ without using numerical methods?
The integrand doesn't seem to converge to anything for any ...
