Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 316 / 3 / c / Solution

For size-independent $Q_D^{\ast }$, the total rate of destructive events whose target exceeds $D$ isSince the integrand is proportional to $D^{\prime 3-2\alpha }$ and $\alpha >3$, the lower limit dominates. With $n(D)=k{D}^{-\alpha }$,The mean interval between such events is therefore