JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\int\limits_0^{\frac{\pi }{3}} {\frac{{\tan \,\,\theta }}{{\sqrt {2k\,\sec \,\theta } }}} \,d\theta \, = \,1 - \frac{1}{{\sqrt 2 }},(k > 0),\) then the value of \(k\) is
- A \(2\)
- B \(\frac {1}{2}\)
- C \(4\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{{\sqrt {2k} }}\int\limits_0^{\pi /3} {\frac{{\tan \theta }}{{\sqrt {\sec \theta } }}} d\theta \) \( = \frac{1}{{\sqrt {2k} }}\int\limits_0^{\pi /3} {\frac{{\sin \theta }}{{\sqrt {\cos \theta } }}} d\theta \)…
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