Mathematics

Problem

Let a curve

y = y(x)

pass through the point

(3, 3)

and the area of the region under this curve, above the x-axis and between the abscissae 3 and

x(>3)

\left(\frac{y}{x}\right)^3

. If this curve also passes through the point

(\alpha, 6\sqrt{10})

in the first quadrant, then

\alpha

is equal to ______ [JEE MAINS - ONLINE - 2022]