I saw this today, I checked in Mathematica and the integral comes out to $\pi$, but I have no idea how to solve it.
FREE Wi-Fi: The Wi-Fi password is the first $10$ digits of the answer. $$\int_{-2}^2\left(x^3\cos\frac x2+\frac12\right)\sqrt{4-x^2}\ dx$$
from Hot Weekly Questions - Mathematics Stack Exchange
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