If g x is a differentiable function such that ∫ 1 sin ⁡ α x 2 g x d x = sin ⁡ α - 1 , ∀ α ∈ 0 , π 2 , then the value of g 1 3 is equal to

Question

If g x is a differentiable function such that ∫ 1 sin ⁡ α x 2 g x d x = sin ⁡ α - 1 , ∀ α ∈ 0 , π 2 , then the value of g 1 3 is equal to, 4, 4 3, 3 2, 9

MARKS App · Accepted Answer

Differentially both sides w.r.t. α , we get sin 2 α ⋅ g sin α ⋅ cos α = cos α ⇒ g sin ⁡ α = 1 sin 2 ⁡ α ∴ g 1 3 = 9

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