Let f(x) be a positive function. Let aligned I₁ & = _ 1-k ^k x f x(1-x) d x, I₂ & = _ 1-k ^k f x(1-x) d x, aligned where 2 k-1 0 , then I₁ I₂ is

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Correct answer: C. 1 2

aligned I₁ & = _ 1-k ^k x f x(1-x) d x & = _ 1-k ^k(1-x) f (1-x)(1-(1-x)) d x & ( _a^b f(x) d x= _a^b f(a+b-x) d x ) & = _ 1-k ^k(1-x) f (1-x) x d x & = _ 1-k ^k f x(1-x) d x - _ 1-k ^k x f x(1-x) d x & I₁=I₂-I₁ 2 I₁=I₂ aligned I₁ I₂ = 1 2

Let f(x) be a positive function. Let aligned I₁ & = _ 1-k ^k x f x(1-x) d x, I₂ & = _ 1-k ^k f x(1-x) d x, aligned where 2 k-1 0 , then I₁ I₂ is

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