The Lower Riemann Sum

The Lower Riemann Sum is formed by taking the maximum function value in the interval and multiplying it by dx. This can be a very difficult sum to calculate, but it can be approximated by:

f(x)*dx if f(x) < f(x+dx) or f(x+dx)*dx if f(x+dx) < f(x)

which simply means "Take the smaller of the endpoint function values and multiply it by dx." This approximation can pose problems for dynamic functions whose maxima and minima are between the endpoints of the interval.