Suppose f,gf,gf,g are continuous functions on [a,b][a,b][a,b] and g≥0g \ge 0g≥0. Then ∃x∈(a,b)\exists x \in (a,b)∃x∈(a,b): f(x)∫abg=∫abfgf(x) \int_a^b g = \int_a^b fgf(x)∫abg=∫abfg