The area of the region bounded by the curve $y = \sin x$ between the abscissa $x = 0, x = \frac{\pi}{2}$ and the X-axis is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $1$ sq units
We have to find area of the region bounded by the curve $y = \sin x$ between the abscissa $x = 0, x = \frac{\pi}{2}$ and the X-axis i.e., $y = 0$.
$∴\text{Required area of shaded region} = \int_{0}^{\pi/2} \sin x \, dx \quad [∵\int \sin x \, dx = -\cos x]$
$= -[\cos x]_{0}^{\pi/2} = -\left[ \cos \frac{\pi}{2} - \cos 0 \right]$
$= -[0 - 1] = 1 \text{ sq. unit}$