All Questions
Tagged with nested-radicals definite-integrals
4
questions with no upvoted or accepted answers
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
1
vote
0
answers
130
views
A very interesting integral: $\int\limits^{2}_{1}\sqrt{x-\sqrt{x!-\sqrt{(x!)!-\sqrt{((x!)!)!-\dots}}}}dx$
I really like infinitely nested radicals so when I was messing around with them in Desmos, I noticed that the domain of $\sqrt{x-\sqrt{x!-\sqrt{(x!)!-\sqrt{((x!)!)!-\dots}}}}$ seemed to converge to $1&...
- 1,688
0
votes
0
answers
114
views
How to evaluate the integral $\int_{-1}^{0}\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{\cdots\sqrt{1+x}}}}}dx=?$
We have :
$$\int_{-1}^{0}\sqrt{1+\sqrt{1+\sqrt{1+x}}}dx=\frac{8}{315}\sqrt{2}\Big(16+\sqrt{233+317\sqrt{2}}\Big)$$
We are lucky because this integral have an anti-derivative like here.
More ...
0
votes
1
answer
99
views
An approximation for an integral involving nested radicals and logarithms
Yesterday I wrote some simple integrals involving nested radicals, and/or continued fractions. This was an example with nested radicals, let $$\int_0^1\frac{dx}{\sqrt{1+(\log x)g(x)}},\tag{1}$$ where $...
user243301