Let I(x) = 6 ^2x(1 - x)^2 dx. If I(0) = 3, then I ( 12 ) is equal to:

JEE Main 2024 Mathematics question

Let . If I(0) = 3, then I is equal to:

Answer: (B)

With t = 1 − cot x, dt = cosec²x dx, so I = ∫6/t² dt = −6/(1 − cot x) + C. I(0) = 3 gives C =

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Question ID VK-012369