To a mathematician, the notation log(x) means the natural log function. To scientists and engineers, the natural log function is denoted ln(x). To avoid confusion, the ln(x) notation will be used here.
If one plots ln(x) over the interval [1,4], one sees that the plot is always less than 2. Thus
[ ln(x) ] is either 0 or 1 on this interval. It is 0 for x < e and 1 for x ≥ e.
The break point at x = e comes about because ln(e) = 1.
The contribution to the integral from the subinterval [1,e] is zero, while the contribution from the subinterval
[e, 4] is 1 x length of this subinterval ( which is 4- e).
Thus the value of the integral is 4 -e
