JEE Advanced 2024 Paper 2 Mathematics Q16

Mathematics

Problem

Paragraph II: Let f : [0, π/2] → [0, 1] be the function defined by f(x) = sin²x and let g : [0, π/2] → [0, ∞) be the function defined by g(x) = √(πx/2 − x²). The value of 2∫₀^(π/2) f(x)g(x)dx − ∫₀^(π/2) g(x)dx is ________.

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