The Upper Riemann Sum
The Upper 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 larger 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.
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