Assume the following fact about integrable functions: If w : [a, b] → R is integrable on [a, b], then its square w² is also integrable on [a, b]. (Recall that w?(x) = w(x)w(x) for x € [a, b].) Prove that if f,g : [a,b] → R are both integrable on [a, b], then their product fg is also integrable on [a, b]. You may use the fact above and any theorems/properties about integration you happen to know, just cite them sensibly.

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