The area (in sq. units) of the region bounded by the curve $y = \sin x,-2π ≤ x ≤ 2π$ and x-axis is equal to

8

The correct answer is Option (3) → 8

Area required is the area between $y=\sin x$ and the $x$-axis from $-2\pi$ to $2\pi$.

$\sin x$ is symmetric about the origin and has equal positive and negative areas in each half period.

Hence area equals four times the area in one positive half cycle from $0$ to $\pi$.

$\text{Area}=4\int_{0}^{\pi}\sin x\,dx$

$=4\left[-\cos x\right]_{0}^{\pi}$

$=4\left[(-\cos\pi)-(-\cos0)\right]$

$=4[(1)-(-1)]$

$=4\times 2=8$

Final answer: $8$ square units