Difficult problem

UzumakiAi

Posers and Puzzles

28 Apr 08

UzumakiAi

Joined: 30 Dec 07
Moves: 9905

28 Apr 08

There is a circle with a diameter of 2. What is the exact average (not in decimal form, but in fraction) of all possible distances between 2 randomly chosen points in the circle?

You have a week. I suspect someone'll get it before then, but I don't know. It was difficult for me to solve.

preachingforjesus

Iron Pillar

Backside of desert

Joined: 09 Nov 06
Moves: 14828

28 Apr 08

4 / pi

using mean value theorem of the integral

I have no idea how to write it here

UzumakiAi

Joined: 30 Dec 07
Moves: 9905

28 Apr 08

Originally posted by preachingforjesus
4 / pi

using mean value theorem of the integral

I have no idea how to write it here

Here is how you would write and integral, with function f(x) of variable x and an interval of [a,b] of the line, the integral would show as this:

int_a^b f(x),dx

which would be equal to the area of a region in coordinate plane bounded by graph of f, the x-axis, and lines x = a and x = b, with areas below the x-axis being subtracted.

Does that help with notation?