The solution for x of the equation _√(2)^x dt/t√(t^2 - 1) = π/12 is: - Mathematics MCQ AIEEE 2007 2026 | ExamTest.live

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The solution for x of the equation \int_{2}^{x} \frac{d t}{t t ^{2} - 1} = \frac{π}{12} is:

Solution & Step-by-step Explanation

We know that \int \frac{d t}{t t ^{2} - 1} = sec^{- 1} t . \int_{2}^{x} \frac{d t}{t t ^{2} - 1} = [sec^{- 1} t]_{2}^{x} = sec^{- 1} x - sec^{- 1} 2 Given this is equal to \frac{π}{12} : sec^{- 1} x - \frac{π}{4} = \frac{π}{12} sec^{- 1} x = \frac{π}{12} + \frac{π}{4} = \frac{π + 3 π}{12} = \frac{4 π}{12} = \frac{π}{3} x = sec (π /3) = 2

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The solution for x of the equation \int_{2}^{x} \frac{d t}{t t ^{2} - 1} = \frac{π}{12} is:

2

π

3/2

22

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