The area (in sq. units) of the region bounded by the curve \(y = \cos x\) between \(x = -\displaystyle\frac{\pi}{2},x=\displaystyle\frac{\pi}{2}\) and the x-axis is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
On \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), \(\cos x \ge 0\), so the curve lies above the x-axis and the area is the integral itself:
\( \displaystyle \text{Area} = \int_{-\pi/2}^{\pi/2} \cos x\,dx \)
\( \displaystyle = \Big[\sin x\Big]_{-\pi/2}^{\pi/2} \)
\(= 1 - (-1) = 2\) sq. units