Draw a rough sketch of the curve $y = \sqrt{x - 1}$ in the interval $[1, 5]$. Find the area under the curve and between the lines $x = 1$ and $x = 5$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{16}{3}$ square units
Given equation of the curve is $y = \sqrt{x - 1}$.
$\Rightarrow y^2 = x - 1$
$∴\text{Area of shaded region} = \int_{1}^{5} (x - 1)^{1/2} \, dx = \left[ \frac{2 \cdot (x - 1)^{3/2}}{3} \right]_{1}^{5}$
$= \left[ \frac{2}{3} \cdot (5 - 1)^{3/2} - 0 \right] = \frac{16}{3} \text{ sq. units}$