Let f (x) be positive for all real x . If I ₁= _ 1- h ^ h x f (x(1-x)) d x and I ₂= _ 1- h ^ h f (x(1-x)) d x , where (2 h-1)0 , then I₁ I₂ is

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Let f (x) be positive for all real x . If I ₁= _ 1- h ^ h x f (x(1-x)) d x and I ₂= _ 1- h ^ h f (x(1-x)) d x , where (2 h-1)>0 , then I₁ I₂ is

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Correct answer: C. 1 2

aligned I ₁ & = _ 1- h ^ h x f (x(1-x)) d x and I ₂ & = _ 1- h ^ h f (x(1-x)) d x I ₁ & = _ 1- h ^ h (1-x) f [(1-x)(1-1+x)] d x [ _ a f (x) d x= _ a ^ b f ( a + b -x) d x ] & I ₁= _ 1- h ^ h (1-x) f (x(1-x)) d x & = _ 1- h ^ h f (x(1-x)) d x- _ 1- h ^ h x f (x(1-x)) d x & I ₁= I ₂- I ₁ & 2 I ₁= I ₂ & I ₁ I ₂ = 1 2 aligned

Let f (x) be positive for all real x . If I ₁= _ 1- h ^ h x f (x(1-x)) d x and I ₂= _ 1- h ^ h f (x(1-x)) d x , where (2 h-1)>0 , then I₁ I₂ is

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