Using integration, find the area of the region bounded by $y = mx (m > 0)$, $x = 1$, $x = 2$ and the $x$-axis.

$\frac{3m}{2}$ sq units

The correct answer is Option (3) → $\frac{3m}{2}$ sq units

Required Area $= \int\limits_{1}^{2} y \, dx$

$= \int\limits_{1}^{2} mx \, dx$

$= \left[ \frac{mx^2}{2} \right]_{1}^{2} = \frac{m(2)^2}{2} - \frac{m(1)^2}{2}$

$= 2m - \frac{m}{2}$

$= \mathbf{\frac{3m}{2} \text{ unit}^2}$