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Continuous Function Integral Product Equality

2425MasterCalculusInequalities

Olimpiada Naţională GAZETA MATEMATICĂ

Determinați funcțiile continue $f:[0,1] \longrightarrow [0, \infty)$ care verifică relația $$ \int_{0}^{1} f(x) \, dx \cdot \int_{0}^{1} f^{2}(x) \, dx \cdots \int_{0}^{1} f^{2020}(x) \, dx = \left(\int_{0}^{1} f^{2021}(x) \, dx\right)^{1010} $$
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