Let \[I(n,a)=\int_{0}^{a}x^ne^{-x}dx\]

Also define, \[T(a)=\lim_{n\rightarrow \infty}(1-\frac{I(n,a)}{n!})e^a\]

Then find the value of \[\int_{0}^{2}T(x)dx\] (correct upto 3 places after the decimal point)

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