Area of the region bounded by the curve $y=\frac{1}{2} \cos x$ and x-axis between x = 0 and x = 2π is:

2 sq. units

The correct answer is Option (1) → 2 sq. units

Area enclosed between x-axis and curve = $\frac{1}{2}\int\limits_{0}^{\pi}\cos x\,dx+\int\limits_{\pi}^{2\pi}\left(-\frac{1}{2}\cos x\right)dx$

$=\frac{1}{2}\left[\sin x\right]_0^{2\pi}$

$=\frac{1}{2}\sin 2\pi$