A particle detector's count rate during a pulse follows

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Calculus of change and accumulation · Calculus of change and accumulation

Mathematical Methods for Physics, Ch Accumulation: integration and the techniques that make it possible

Problem

A particle detector's count rate during a pulse follows r(t)=r0 (t/τ) e−t2/τ2r(t) = r_0\,(t/\tau)\,e^{-t^2/\tau^2}, where r0=1000 s−1r_0 = 1000\,\mathrm{s^{-1}} sets the size of the rate and τ=1.0 s\tau = 1.0\,\mathrm{s} its duration. Find the total number of counts recorded between t=0t=0 and t=τt=\tau, that is, N=∫0τr(t) dtN = \displaystyle\int_0^{\tau} r(t)\,\mathrm{d}t.

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