If gx is a differentiable function such that ∫1sin⁡αx^2gxdx=sin⁡α-1, ∀α∈0,(π)/2, then the value of g1/3 is equal to

Question

MARKS Content Team · Accepted Answer

Correct answer: (D) 9. Differentially both sides w.r.t. α , we get sin^2 α⋅g sinα ⋅cosα=cosα ⇒gsin⁡α=1/(sin^2⁡α) ∴g1/3=9

If $g (x)$ is a differentiable function such that $\int_{1}^{\sin α} x^{2} g (x) d x = (\sin α - 1), \forall α \in (0, \frac{π}{2}),$ then the value of $g (\frac{1}{3})$ is equal to