Compute and data grids: class #11
(1)
\begin{align} \int_0^{t_\infty} u \widetilde{f_R}(u) du = \left[u \widetilde{F_R}(u)\right]_0^{t_\infty} - \int_0^{t_\infty} \widetilde{F_R}(u) du = t_\infty\widetilde{F_R}(t_\infty) - \int_0^{t_\infty} \widetilde{F_R}(u) du \end{align}
(2)
\begin{align} \frac{1}{\widetilde{F_R}(t_\infty)}t_\infty\widetilde{F_R}(t_\infty) - \frac{1}{\widetilde{F_R}(t_\infty)}\int_0^{t_\infty} \widetilde{F_R}(u) du + \frac{t_\infty}{\widetilde{F_R}(t_\infty)} = -\frac{1}{\widetilde{F_R}(t_\infty)}\int_0^{t_\infty}\widetilde{F_R}(u) du + \frac{1}{\widetilde{F_R}(t_\infty)}\int_0^{t_\infty}du = \frac{1}{\widetilde{F_R}(t_\infty)} \int_0^{t_\infty}(1 - \widetilde{F_R}(t_\infty))du \end{align}
Unclear, need to ask the teachers, since most is obviously derived works.