Question #41166

This question constructs a 'Lethal Collision' by nesting an inverse trigonometric identity within a modulus function, combined with an odd-function distractor.

The primary trap is the assumption that $\sin^{-1}(\sin x) = x$ over the entire domain $[-2\pi, 2\pi]$, which would lead to an incorrect integration of $|x^2 - \pi^2/16|$.

To solve it efficiently, students must sequentially apply even/odd symmetry, identify the $\pi$-periodicity of the squared inverse function, and use reflection symmetry about $\pi/2$ to restrict the domain to $[0, \pi/2]$.

Finally, they must correctly split the integral at the modulus root $x = \pi/4$, testing their precision in handling non-differentiable points within simplified intervals.