If f x is a non-negative function such that the area bounded by y = f x , x -axis and the lines x = 0 and x = α is 4 α sin ⁡ α + 2 sq. units ∀ α ∈ 0 , π , then the value of f π 2 is equal to

Question

If f x is a non-negative function such that the area bounded by y = f x , x -axis and the lines x = 0 and x = α is 4 α sin ⁡ α + 2 sq. units ∀ α ∈ 0 , π , then the value of f π 2 is equal to, 0, 4, 2 π, 8 π

MARKS App · Accepted Answer

Given, ∫ 0 α f x d x = 4 α sin ⁡ α + 2 On differentiating with respect to α , we get, f α = 4 α ⋅ cos α + 4 sin α ∴ f π 2 = 4

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