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JEE Mains · Maths · STD 12 - 7.2 definite integral
The integral \(\int\limits_{7\pi /4}^{7\pi /3} {\sqrt {{{\tan }^2}\,x}\,dx } \) is equal to
- A \(\log \,\,2\sqrt 2 \)
- B \(\log \,\,2 \)
- C \(2\log \,\,2 \)
- D \(\log \,\,\sqrt 2 \)
Answer & Solution
Correct Answer
(D) \(\log \,\,\sqrt 2 \)
Step-by-step Solution
Detailed explanation
\({\rm{Let }}I = \int\limits_{7\pi /4}^{7\pi /3} {\sqrt {{{\tan }^2}x} dx} \) \(\int\limits_{7\pi /4}^{7\pi /3} {\tan xdx} \) \(= - \left. {\log \cos x} \right|_{7\pi /4}^{7\pi /3}\) \(=-\left[\log \cos \frac{7 \pi}{3}-\log \cos \frac{7 \pi}{4}\right]\)…
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