j****i
发帖数: 305 | 1 Int[Delta(g(s)),{s,s0-,s0+}] = Int[Delta(y)/g'(s),{s,0.0+}],use y = g(s),
dy = g'(s)ds. | y***u
发帖数: 25 | 2 Set t=g(s)=>s=G[t], where g and G are inverse functions
so for an arbitrary function continuous f(s)
Int[[Delta[g(s)]*f(s) ds=Int[Delta[t]*f[G(t)] dt/g'[G(t)]]
=f[G(0)]/g'[G(0)]=f(s0)/g'[s0]
since f[s] is an arbitrary continous function=>Delta(g(s))=Delta(s-s0)/g'(s0) |
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