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let f:R->R be a continuous function which satisfies
f(x) = \int_{0}^{x}{f(t)dt}
then the value of f(ln 5) is
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9 Answers
66f(x)=\int_0^xf(t)\ \mathrm{d}t
Differentiating w.r.t. x, we get
f^\prime(x)=f(x)
Therefore, f(x)=Ce^x
Since f(0)=0, we get C=0. Therefore
f(x)\equiv 0 for all x.
Hence f(ln 5)=0
