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JEE Main 2014

JEE Main 2014 Mathematics question on Definite Integrals and Areas

The integral ∫0π21+4sin⁡2x2−4sin⁡x2 dx\int\limits_0^{\frac{\pi}{2}} \sqrt{1 + 4\sin^2\frac{x}{2} - 4\sin\frac{x}{2}}\, dx is equal to
  1. A.
    π−4\pi - 4
  2. B.
    2π3−4−43\frac{2\pi}{3} - 4 - 4\sqrt{3}
  3. C.
    43−44\sqrt{3} - 4
  4. D.
    43−4−π/34\sqrt{3} - 4 - \pi/3
Show answer

Correct option: D

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