tl;dr yes. I just spent the past few minutes trying to reverse engineer it. I'm no expert, but here's how I figure things. For the left side of the equation: T

tl;dr yes. I just spent the past few minutes trying to reverse engineer it. I'm no expert, but here's how I figure things. For the left side of the equation: The formula for a circle's area is a = PI r^2. For a unit circle, the area is simply equal to PI. Now for the right side of the equation: r^2 = x^2 + y^2 is the Pythagorean Theorem and also the equation of a circle. If we solve for y, we have y = sqrt(r^2 - x^2). In other words, the height of any circle (centered at the origin) is sqrt(r^2 - x^2) given any particular place along the x-axis. This is the same expression which is integrated. For a unit circle, we assume r = 1 and ignore everything outside of -1 and 1 on the x-axis. This is why the integral is bound between -1 and 1. So now we have integrate(-1, 1){ sqrt(1^2 - x^2) }. By integrating we get the area of the top half of the unit circle. But we also need the bottom half. So we just double everything and that's what the extra 2 is for. We now have the area of a unit circle on the right side too. QED