Let $f(x)$ be a positive function and $I_1=\int_{-\frac{1}{2}}^1 2 x f(2 x(1-2 x)) d x$ and $I_2=\int_{-1}^2 f(x(1-x)) d x$. Then the value of $\frac{I_2}{I_1}$ is equal to [JEE Main 2025, 8 Apr (Shift 1)]

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Let \(f(x)\) be a positive function and \(I_1=\int_{-\frac{1}{2}}^1 2 x f(2 x(1-2 x)) d x\) and \(I_2=\int_{-1}^2 f(x(1-…

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