[bizaro86]

Originally Posted by SebC

full solution, I think, piggybacking on what bizaro86 has already explained about the first half of the function:

Spoiler!

A circle is x^2+y^2=r^2

y^2=r^2-x^2

y=sqrt(r^2-x^2)

y=sqrt(4-x^2) is a semi-circle of radius 2

integral of y=sqrt(4-x^2) from -2 to 2 is half of the area of a circle of radius 2 (because the bottom half is negative)

area of a circle is pi*r^2, in this case pi*4... half of that is pi*2

but the function we're integrating is y=1/2*sqrt(4-x^2), which is half as tall, so the area under the curve is also halved

so the answer to the full integral included the odd and even parts is pi

wifi password is 314 or something similar, though you still have to brute force it a bit because the cafe didn't say how many digits are required

which probably would've been in everyone's top few guesses anyways

psyang: What drives your interest in all this? Are you a math teacher professionally? I'm just curious.

Well once you put it like that it seems obvious! Nice work.

Spoiler!

Although I did post the answer by inference in post 187!