Unbeatable area

Calculus Level 3

Let the area bounded by the function f(x)=max(sin(x),cos(x)) f(x) = \max(\sin(x), \cos(x)) and the xx-axis on the interval 0xπ2 0 \leq x\leq \frac\pi2 be kk, find the value of k4k^4.

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