Calculus Mixed Practice: JEE Advanced MCQ

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JEE AdvancedHardQuestion 430005

Question

If ∫₀^a x dx = ∫ₐ^1 x dx, then a equals:

1/√2

∫₀^a x dx = a²/2. ∫ₐ^1 x dx = (1−a²)/2. Setting equal: a²/2 = (1−a²)/2 → a² = 1−a² → 2a² = 1 → a = 1/√2.