Let f(x) be a positive function and I₁ = ∫ -1/2 ¹ 2x f(2x(1 - 2x)) dx and I₂ = ∫₋₁^(1/2) f(x(1 - x)) dx. Then the value of I₂/I₁ is equal to:

Integral Calculus: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q208

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002

Let

f(x)

be a positive function and

I_1 = \int_{-\frac{1}{2}}^{1} 2x f(2x(1 - 2x)) \, dx \quad \text{and} \quad I_2 = \int_{-1}^{\frac{1}{2}} f(x(1 - x)) \, dx.

Then the value of

\frac{I_2}{I_1}

is equal to:

JEE Main 2025 Integral Calculus Question with Solution (April Unspecified (session-level dataset), Q208) | JEE Arc

JEE Main 2025 · April, Unspecified (session-level dataset) · Q208

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002

Let

f(x)

be a positive function and

I_1 = \int_{-\frac{1}{2}}^{1} 2x f(2x(1 - 2x)) \, dx \quad \text{and} \quad I_2 = \int_{-1}^{\frac{1}{2}} f(x(1 - x)) \, dx.

Then the value of

\frac{I_2}{I_1}

is equal to: