Continuous Function Integral Identity

2175ExpertCalculusFunctions

64th Romanian Mathematical Olympiad - Final Round

Find all continuous functions $f: \mathbb{R} \to \mathbb{R}$ having the property that $(a^2 + ab + b^2) \int_a^b f(x) \, dx = 3 \int_a^b x^2 f(x) \, dx$, for all $a, b \in \mathbb{R}$.

0 students attempted0% solvedRating 2175

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Continuous Function Integral Identity

2175ExpertCalculusFunctions

64th Romanian Mathematical Olympiad - Final Round

Find all continuous functions $f: \mathbb{R} \to \mathbb{R}$ having the property that $(a^2 + ab + b^2) \int_a^b f(x) \, dx = 3 \int_a^b x^2 f(x) \, dx$, for all $a, b \in \mathbb{R}$.

0 students attempted0% solvedRating 2175