In applications it is sometimes useful to use an approximation for factorials. The factorial of a positive integer n is defined to be the number n! = 1 · 2 · 3.. (n – 1) · n, e.g., 4! = 1 · 2 · 3·4 = 24. Noticing that F(x) = x ln x – x is an antiderivative of f(x) =In x, use the definition of the definite integral (Riemann sums) to show that In(n!) = n In n – n. is a good approximation of ln(n!) for large values of n.

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