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

Given that,
$y = 2\cos x,0 \le x \le 2\pi$

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From the figure, we need to find the area of the region(OABCDEF)

$A = \int_0^{2x} | 2\cos x|dx$

$= 4\int_0^{\pi 2} {(2\cos x)} dx = 8(\sin x)_0^{\sqrt 2 } = 8$ sq. units