The area (sq.units) bounded by the curve $y = \sin x,π ≤ x ≤ 2π$ and the x-axis is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2
Given: $y = \sin x$, interval: $x \in [\pi, 2\pi]$
On $[\pi, 2\pi]$, $\sin x \leq 0$
Required area = $\int_{\pi}^{2\pi} | \sin x | \, dx = - \int_{\pi}^{2\pi} \sin x \, dx$
$= - [ -\cos x ]_{\pi}^{2\pi} = \cos \pi - \cos(2\pi)$
$= (-1) - (1) = -2$
Area = ${2}$ sq. units