Life expectancy expected value

Calculus Level 4

\[f(x)=\frac{\pi}{14400}x\sin\left(\frac{\pi}{120}x\right),\ \ 0<x<120\]

A life insurance actuary estimates probabilities of \(X\), a person's life expectancy, with the probability density function as described above.

According to this model, what is \(\lfloor \text{E}[X]\rfloor\)?

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