Monte Carlo Integration - determining if a random x,y coordinate falls within the circle or square My textbook says you can take any random (x,y )coordinate between -1 and 1  like (-.3, .5) or (.4, -.7) and determine if the given coordinate falls within the circle if you calculate $\sqrt(x^2+y^2)$ < 1.   
The part I don't understand is why are you testing the (x,y) coordinate against 1? What is the rationale behind squaring x and y and seeing if it is less than 1? How do you arrive at 1?
Also do you typically only use -1 and 1 when you're dealing with Monte Carlo integration or can you use -5 and 5 or -10 or 10 or any other numbers? 

The equation $\sqrt{x^2+y^2}<1$ is just the equation of a circle of radius one, and the box between $\pm 1$, is just a convenient bounding box who's area is known. This can be extended arbitrarily, for instance, to calculate the area of between the function $\sin x$ and the $x$ axis between $0$ and $\pi/2$, you can use a Monte Carlo method and generate points with $x \in [0,\pi/2]$ and $y \in [0,1]$. 
