Find the area bounded by the curve $y = 2 \cos x$ and the X-axis from $x = 0$ to $x = 2\pi$.

$8$ square units

The correct answer is Option (3) → $8$ square units

Required area of shaded region $= \int\limits_{0}^{2\pi} 2 \cos x \, dx$

$= \int\limits_{0}^{\pi/2} 2 \cos x \, dx + \left| \int\limits_{\pi/2}^{3\pi/2} 2 \cos x \, dx \right| + \int\limits_{3\pi/2}^{2\pi} 2 \cos x \, dx$

$= 2 [\sin x]_{0}^{\pi/2} + \left| 2 (\sin x)_{\pi/2}^{3\pi/2} \right| + 2 [\sin x]_{3\pi/2}^{2\pi}$

$= 2 + 4 + 2 = 8 \text{ sq. units}$