First slide

Evaluation of definite integrals

Question

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

Easy

A

4
B

2
C

6
D

$\sqrt{3}$

Solution

$\int_{\sqrt{2}}^{x} \frac{1}{t \sqrt{t^{2} - 1}} d t = \frac{π}{12}$
$\Rightarrow {(S e c^{- 1} t)}_{\sqrt{2}}^{x} = \frac{π}{12}$

$\Rightarrow S e c^{- 1} x - \frac{π}{4} = \frac{π}{12}$

$\Rightarrow S e c^{- 1} x = \frac{π}{3} \Rightarrow x = 2$

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