# 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

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

Inspiration

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