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Let the area bounded by the function f(x)=max(sin(x),cos(x)) f(x) = \max(\sin(x), \cos(x)) f(x)=max(sin(x),cos(x)) and the xxx-axis on the interval 0≤x≤π2 0 \leq x\leq \frac\pi20≤x≤2π be kkk, find the value of k4k^4k4.
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