An identity (Putnam Exam 1941) Let f be a continuous

Chapter 12, Problem 62AE

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An identity (Putnam Exam 1941) Let f be a continuous function on [0, 1]. Prove that

\(\int_{0}^{1} \int^{1} \int_{x}^{y} f(x) f(y) f(z) d z d y d x=\frac{1}{6}\left(\int_{0}^{1} f(x) d x\right)^{3} .\)

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