If , , and are continuous functions on such that , , and , then the value of…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

If ff, gg, and hh are continuous functions on [0,a][0,a] such that f(a−x)=f(x)f(a-x)=f(x), g(a−x)=−g(x)g(a-x)=-g(x), and 3h(x)=5+4h(a−x)3h(x)=5+4h(a-x), then the value of ∫0af(x)g(x)h(x) dx\int_0^a f(x)g(x)h(x)\,dx is (1) 0 (2) 1 (3) aa (4) 2a2a

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