A) \[\frac{\sqrt{3}}{2}\]
B) \[2\sqrt{2}\]
C) \[-\sqrt{2}\]
D) \[\pi \]
Correct Answer: C
Solution :
[c] : We have, \[\int\limits_{\sqrt{2}}^{x}{\frac{dt}{t\sqrt{{{t}^{2}}-1}}}=\frac{\pi }{2}\] \[\Rightarrow \]\[\left[ {{\sec }^{-1}}t \right]_{\sqrt{2}}^{x}=\frac{\pi }{2}\] \[\Rightarrow \]\[{{\sec }^{-1}}x-{{\sec }^{-1}}\sqrt{2}=\frac{\pi }{2}\Rightarrow {{\sec }^{-1}}x=\frac{\pi }{2}+\frac{\pi }{4}=\frac{3\pi }{4}\] \[\Rightarrow \]\[x=-\sqrt{2}\].
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