Let f(x) be a positive function and I₁ = ∫_(-1/2)¹ 2x f(2x(1-2x))… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 8 April, Shift 2Integration Techniques (Substitution, Parts, Partial Fractions)

Let $f(x)$ be a positive function and $I_1 = \int_{-\frac{1}{2}}^1 2x \, f\left(2x(1-2x)\right) \, dx$ and $I_2 = \int_{-1}^2 f\left(x(1-x)\right) \, dx.$ Then the value of $\frac{I_2}{I_1}$ is equal to _____

A
$4$
B
$6$
C
$12$
D
$9$

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