2/$\pi $ * $\int $(x=0 to 1) cos^{-1}(x) dx =

2/$\pi $ * [x*cos^{-1}(x) - (1-x^{2})^{1/2} for (x=0 to 1)] =

2/$\pi $ * (0-0-0+1) =

2/$\pi $ =~ 0.636620

Thanks to Extra Stuff: Gambling Rambling by Peter Griffin for this problem. See chapter 11.

Michael Shackleford, ASA, August 20 1999