Commemorating Victory Day, May 9, 1945

Calculus Level 5

If \(f(x)\) is a polynomial with real coefficients such that

\[\int_{0}^{1}f(x)x^k \, dx=1\]

for \(k=0,1,2,..., 1945\), find the minimal value of

\[\int_{0}^{1}(f(x))^2 \, dx . \]


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