AP EAMCET · Maths · Definite Integration
The value of \(x\) that satisfies the equation \(\int_{\sqrt{2}}^x \frac{d t}{|t| \sqrt{t^2-1}}=\frac{\pi}{12}\) is
- A 1
- B 0
- C \(-\sqrt{2}\)
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \int_{\sqrt{2}}^x \frac{d t}{|t| \sqrt{t^2-1}}=\frac{\pi}{12} \\ & \Rightarrow \quad\left[\sec ^{-1} t\right]_{\sqrt{2}}^x=\frac{\pi}{12} \Rightarrow \sec ^{-1} x-\sec ^{-1} \sqrt{2}=\frac{\pi}{12} \\ & \Rightarrow \quad \sec ^{-1}…
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