Riddles, brain puzzles and mathematical problems

[BAndrew]

Hahahaha

I have another riddle/problem, but I haven't solved it yet. I'll inform you when I have. I'll start trying it now.


EDIT:

Spoiler below!

OH MY GOD! I solved it! The problem is REALLY hard. If I didn't know calculus I wouldn't be able to solve it. The problem requires some Math knowledge. I don't know if anyone wants to try, but whatever, here's the problem. I will provide the knowledge you probably don't have.

Problem:
Consider a bone with length 1. We break it randomly in two pieces*. Find the average value of the ratio of the length of the largest to the smallest piece.

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in other words find the
average = length of large piece / length of small piece

I am not here to test how good or bad you are at math so here are the
Things you need to know, but probably don't:

The middle value of a continuous function f is:



How to calculate an integral:
If you don't already know then it is not so simple so go here
and type:
integral from "bottom_number" to "top_number" of "write_function_here" dx

With the help I provided you should be able to solve it like a normal problem.

*It is equally likely to break it on any point.

When I first saw it I thought it didn't have so advanced math, but I was plane wrong.