Q96 / 160 · WBJEE 2010 · Mathematics

$\int \sqrt{1+\cos x} d x$ is equal to

  • A
    $2 \sqrt{2} \cos \frac{\mathrm{x}}{2}+\mathrm{C}$
  • Correct answer
    B
    $2 \sqrt{2} \sin \frac{\mathrm{x}}{2}+\mathrm{C}$
  • C
    $\sqrt{2} \cos \frac{x}{2}+C$
  • D
    $\sqrt{2} \sin \frac{x}{2}+C$

Solution

Hints: $\int \sqrt{1+\cos x} d x=\sqrt{2} \int \cos \left(\frac{x}{2}\right) d x=2 \sqrt{2} \sin \left(\frac{x}{2}\right)+c$

Hence, the correct answer is option: 'B'.

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