Question

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

Answer 1

Required area of shaded region $={\int }_0^{2\pi }2\cos xdx$

$={\int }_0^{\pi /2}2\cos xdx+|{\int }_{\pi /2}^{3\pi /2}2\cos xdx|+{\int }_{3\pi /2}^{2\pi }2\cos xdx$

$=2[\sin x{]}_0^{\pi /2}+|2(\sin x{)}_{pi/2}^{3\pi /2}|+2[\sin x{]}_{3\pi /2}2\pi$

$=2+4+2=8squnits$.