Question
If the area of the region $S=\left\{(x, y): 2 y-y^{2} \leq x^{2} \leq 2 y, x \geq y\right\}$ is equal to $\frac{n+2}{n+1}-\frac{\pi}{n-1}$, then the natural number $n$ is equal to ___________.
Correct Answer
5
If the area of the region $S=\left\{(x, y): 2 y-y^{2} \leq x^{2} \leq 2 y, x \geq y\right\}$ is equal to $\frac{n+2}{n+1}-\frac{\pi}{n-1}$, then the natural number $n$ is equal to ___________.