EugeneKudashev wrote:I'm not following, your logic is sort of obscure (no offense).
first, you write 't' in the end of integrand, while it should be 'dt', but that's minor.
what is more significant is that you write f(x), but your right-hand side depends only on variable t, and the same is for F(x).
try again, please.
p.s. there's a very neat way how to solve this [easy] problem even w/o L'Hopital.
notice that you work with very little x (x -> 0), and recall that for such x "sin(x) ~= x" holds true. thus, the initial integral becomes
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