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

Step-by-step solution

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