Question: Find all continuous functions(if any) defined on [0,1], so that integral from 0 to 1 f(x)dx =1, integral from 0 to 1 f(x)sin(x)dx= a, integral

Find all continuous functions(if any) defined on [0,1], so that integral from 0 to 1 f(x)dx =1, integral from 0 to 1 f(x)sin(x)dx= a, integral from 0 to 1 f (x) sin²(x)dx=a²

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