Chapter 9.1, Problem 6CP

Use $n={10}^4$

pseudo-random points to estimate the interior volume of the ellipsoid defined by $2+4x^2+4z^2+y^2\le 4x+4z+y$, contained in the unit cube $0\le x,y,z\le 1$ . Compare your estimate with the correct volume $\pi /24$, and report the error. Repeat with $n={10}^6$ points.