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JEE Main 2026 Mathematics question

MathematicsArea Under CurveJEE Main 2026

Let f : ℝ → ℝ be a function such that f(x)+3f(π/2−x)=sinx, x∈ℝ. Let the maximum value of f on ℝ be α. If the area of the region bounded by the curves g(x)=x² and h(x)=βx³, β>0, is α², then 30β³ is equal to .

Answer: 16

Solution

Solving the functional equation gives f(x)=(3cosx−sinx)/8, with maximum

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Question ID VK-015433