1. Using the trapezoid Approximation rather than endpoints does a better job (average of left and right) Z n 1 lnx dx ˇ Xn k=2 ln(k 1)+ln(k) 2 = ln(n!) 1 2 ln(n) This unrolls to the Approximation (note: arithmetic mean of logs is geometric mean without logs): n! ˇ(n=e)ne p n Correct except numerical factor: e vs