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Let $f: \mathbb{R} \to \mathbb{R}$ be a function such that $f(x) + 3f\left( \frac{\pi}{2} - x \right) = \sin x, x \in \mathbb{R}$. Let the 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 :}
Let $f: \mathbb{R} \to \mathbb{R}$ be a function such that $f(x) + 3f\left( \frac{\pi}{2} - x \right) = \sin x, x \in \mathbb{R}$. Let the 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 :}
Updated On: Apr 12, 2026
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Correct Answer: 16
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