Can anyone construct a nonzero continuous function $f:[0, 1]\times[0, 1]\times [0, 1]\rightarrow [0, \infty)$ such that \begin{equation*} \int_{t_1=0}^1 \int_{t_2=0}^1 \int_{t_3=0}^1 f(t_1, t_2, t_3)~ \Big(t_1 + t_3 - 5\Big) \mathrm{d}t_3\mathrm{d}t_2\mathrm{d}t_1 = 0~? \end{equation*}
2026-04-26 03:02:31.1777172551
A Question On Triple Integration
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As $t_1 + t_3 - 5\le 1 + 1 - 5 = -3$ in the integration domain, is impossible.