Life expectancy expected value

Expected Value of the pdf:

$\text{E}[X]=\int_{0}^{120}{xf(x)\ dx}= \int_{0}^{120}{\frac{\pi}{14400}x^2\sin\left(\frac{\pi}{120}x\right)\ dx}$

Using integration by parts , this is:

$\text{E}[X]=\left. -\frac{1}{120}x^2\cos\left(\frac{\pi}{120}x\right)+\frac{2}{\pi}x\sin\left(\frac{\pi}{120}x\right)+\frac{240}{\pi^2}\cos\left(\frac{\pi}{120}x\right)\right |_{0}^{120}$

This evaluates to:

$\text{E}[X]=120-\frac{480}{\pi^2}\approx 71.366$

Thus, $\lfloor \text{E}[X]\rfloor =\boxed{71}$ .