Find the area bounded by the curve $y = \cos x$ between $x = 0$ and $x = 2\pi$.

4

The correct answer is Option (3) → 4

From Figure, the required area $=$ area of the region OABO $+$ area of the region BCDB $+$ area of the region DEFD.

Thus, we have the required area:

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

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

$= 1 + 2 + 1 = 4$