First slide

Evaluation of definite integrals

Question

The solution of the equation
$\int_{\sqrt{2}}^{x} \frac{d x}{x \sqrt{x^{2} - 1}} = \frac{π}{12}$ is given by

Moderate

A

1
B

2
C

3
D

$\sqrt{3}$

Solution

$\begin{array}{l} \int_{\sqrt{2}}^{x} \frac{d t}{t \sqrt{t^{2} - 1}} = \frac{π}{12} \\ \Rightarrow \sec^{- 1} x - \sec^{- 1} \sqrt{2} = π / 12 \\ \Rightarrow \sec^{- 1} x = π / 3 \\ \Rightarrow x = \sec (π / 3) = 2 \end{array}$

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