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The number of positive continuous f(x) d...

The number of positive continuous `f(x)` defined in `[0,1]` for with `I_(1)=int_(0)^(1)f(x)dx=1,I_(2)=int_(0)^(1)xf(x)dx=a`,
`I_(3)=int_(0)^(1)x^(2)f(x)dx=a^(2)` is /are

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