Help with Wi-Fi password

Quote: Ace2

It is a good thing the password doesn't require all of the digits. I only know the first six digits without looking it up.

Is the answer pi?

EDIT: Ha.... It is.

Quote: TigerWu

Is the answer pi?

EDIT: Ha.... It is.

It was too obvious without the math when they mentioned the first 10 digits. If it was something else, I'd go to McDonalds.

Is it only solvable numerically or is there an analytic solution? And does anyone know how to solve it analytically?

Quote: gordonm888

Is it only solvable numerically or is there an analytic solution? And does anyone know how to solve it analytically?

Well, the graph y = sqrt(4 - x²) from -2 to 2 is a semicircle of radius 2, which has area 2 PI.
Rewrite the value as two integrals from -2 to 2: x³ cos (x/2) sqrt(4 - x²) dx, and 1/2 sqrt(4 - x²) dx.
The latter is 1/2 x 2 PI = PI.
For the former, cos (x/2) and sqrt(4 - x²) are reflected through the y-axis, while x³ is reflected through the origin, so the entire value should be reflected through the origin, which means the integral would be zero because it covers the same x values on each side.

That's about as close to an analytic solution that I can come up with at the moment.

Quote: gordonm888

Is it only solvable numerically or is there an analytic solution? And does anyone know how to solve it analytically?

Using https://www.integral-calculator.com , the integral (“computed by maxima”) is:

(x(4 - x^2)^.5 + 4arcsin(x/2)) / 4 + C