MathGroup Archive 2003

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use of SetDelayed functions in Plot and Solve

Why can't I plot the function and find the solution to the equation below
using SetDelayed functions?  Below is just an example, the real functions
are symbolically non-integrable.

s[t_] :=NIntegrate[t^2 - z*Log[t] , {z, 0, k[t]}]
i[t_] := D[s[t],t] /. {k[t] ->2t,k'[t]->Sin[t]}
Plot[i[t], {t, 1, 10}]
Solve[i[t]==300, t]]

All I get is an empty graph because I have "not machine real size numbers"
and my equation "appears to be solved essentially in non-algebraic way".
If I rewrite the code using simple Set I get my graph and solutions.

s=Integrate[t^2 - z*Log[t] , {z, 0, k[t]}]
i=D[s,t] /. {k[t]->2t,k'[t]->Sin[t]}
Plot[i, {t, 1, 10}]
Solve[i==300, t]]

Very confused. Thanks, Mukhtar Bekkali

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