JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+\) constant, then \(\beta-\alpha\) is equal to
- A \(0.5\)
- B \(1\)
- C \(10\)
- D \(100\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\(\int \sqrt{\sec 2 x-1} d x=\int \sqrt{\frac{1-\cos 2 x}{\cos 2 x}} d x\) \(=\sqrt{2} \int \frac{\sin x}{\sqrt{2 \cos ^2 x-1}} d x\) \(\text { put } \cos x=t \Rightarrow-\sin x d x=d t\) \(=-\sqrt{2} \int \frac{d t}{\sqrt{2 t^2-1}}\)…
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