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∫(f(x) - g(x))dx from a to b if f(x)≥g(x) for all x in [a,b].

My question is.. if I were given two function f and g in a given interval [a,b], what is the best way to dertermine if f(x)≥g(x) or vise versa? Would it be best to graph the two functions then visually evaluate it?

Im looking for better methods... any suggestions??