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

JEE Main · 2007 · 29 Apr 2007 · Offline · Definite Integrals

The solution for x of the equation

\int_{2}^{x} \frac{d t}{t t ^{2} - 1} = \frac{π}{12}

Answer: (A)

The integrand integrates to

sec^{- 1} t

, so

sec^{- 1} x - sec^{- 1} 2 = \frac{π}{12}

. Since

sec^{- 1} 2 = \frac{π}{4}

, this gives

sec^{- 1} x = \frac{π}{4} + \frac{π}{12} = \frac{π}{3}

, hence

x = sec \frac{π}{3} = 2

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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