MathsJEE Main 5 Apr 2026, Shift 2·Q24·Numerical·Tough

Area under Curves · Area between curves

Let

f : \mathbb{R} \to \mathbb{R}

be a function such that

f(x) + 3f\left(\dfrac{\pi}{2} - x\right) = \sin x

,

x \in \mathbb{R}

. Let maximum value of

f

on

\mathbb{R}

be

\alpha

. If the area of the region bounded by the curves

g(x) = x^2

and

h(x) = \beta x^3

,

\beta > 0

, is

\alpha^2

, then

30\beta^3

is equal to .

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