The value of $x$ that satisfies the equation $\int_{\sqrt{2}}^x \frac{d t}{| t| \sqrt{t^2-1}}=\frac{\pi}{12}$ is

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Aicharya · Accepted Answer

$\begin{aligned} & \int_{\sqrt{2}}^x \frac{d t}{|t| \sqrt{t^2-1}}=\frac{\pi}{12} \ & \Rightarrow \quad\left[\sec ^{-1} tight]_{\sqrt{2}}^x=\frac{\pi}{12} \Rightarrow \sec ^{-1} x-\sec ^{-1} \sqrt{2}=\frac{\pi}{12} \ & \Rightarrow \quad \sec ^{-1} x=\frac{\pi}{12}+\frac{\pi}{4}=\frac{\pi}{3} \ & \Rightarrow \quad x=\sec \left(\frac{\pi}{3}ight)=2 \end{aligned}$

The value of \(x\) that satisfies the equation \(\int_{\sqrt{2}}^x \frac{d t}{| t|…

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