Hi folks, I know its a long shot, but would anyone like to explain how to integrate the function
f(x) = 2/(pi * r^2) sqrt(R^2 - x^2)
I'm sorry about the poor notation. Please see Wigner semicircle distribution - Wikipedia, the free encyclopedia for a clearer idea.
It's been a long time since I've done integration. I presume it involves a substitution like, say, u = R^2 - x^2. I just can't seem to figure it out.
Got any ideas?
Alternatively since
Just represents the integration of a semi-circle of radius r multiplied by a contant. And since integration is equivalent to finding area we can see that
So
Now if
if
then
NOTE this only applies to if the integration limits are -r and r...that is what I have gathered...if they are not DO NOT APPLY this....even if they are not I hope this has helped gap a bride between integration and area and how sometimes we dont eve need to integrate