JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\mathop \smallint \limits_0^\pi \sqrt {1 + 4{{\sin }^2}\frac{x}{2} - 4\sin \frac{x}{2}} \;dx = \)
- A \(4\sqrt 3 - 4\)
- B \(\;4\sqrt 3 - 4 - \frac{\pi }{3}\)
- C \(\pi - 4\;\)
- D \(\frac{{2\pi }}{3} - 4\sqrt 3 - 4\)
Answer & Solution
Correct Answer
(B) \(\;4\sqrt 3 - 4 - \frac{\pi }{3}\)
Step-by-step Solution
Detailed explanation
\(\int\limits_0^\pi {\left| {\left( {1 - 2\sin \frac{x}{2}} \right)} \right|} dx\) \( = \int\limits_0^{\frac{\pi }{3}} {\left| {\left( {1 - 2\sin \frac{x}{2}} \right)} \right|} dx - \int\limits_{\frac{\pi }{3}}^\pi {\left| {\left( {1 - 2\sin \frac{x}{2}} \right)} \right|} dx\)…
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