Let _ ^ _e4 dx e^x - 1 = 6. Then eᵅ and e⁻ᵅ are the roots of the equation:

JEE Main 2024 Mathematics question

Let . Then eᵅ and e⁻ᵅ are the roots of the equation:

Answer: (A)

An antiderivative is 2tan⁻¹√(eˣ − 1). At log 4: 2·(π/3); so 2π/3 − 2tan⁻¹√(eᵅ − 1)

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Question ID VK-012463