Chapter 9.1, Problem 5CP

Use $n={10}^4$

pseudo-random points to estimate the interior area of the ellipses

(a) $13x^2+34xy+25y^2\le 1$ in $-1\le x,y\le 1$ and (b) $40x^2+25y^2+y+9/4\le 52xy+14x$ in $-1\le x,y\le 1$ . Compare your estimate with the correct areas (a) $\pi /6$ and (b) $\pi /18$, and report the error of the estimate. Repeat with $n={10}^6$ and compare results.