The area (sq.units) bounded by the curve \(y = \sin x, \pi \le x \le 2\pi\) and the x-axis is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2
For \(\pi \le x \le 2\pi\), \(\sin x \le 0\): the curve lies below the x-axis, so the area is the absolute value of the integral:
\( \displaystyle \int_{\pi}^{2\pi} \sin x\,dx = \left[-\cos x\right]_{\pi}^{2\pi} \)
\( \displaystyle \int_{\pi}^{2\pi} \sin x\,dx = -\cos 2\pi + \cos \pi = -1 - 1 = -2 \)
\(\text{Area} = |-2| = 2\)