The area (in sq. units) of the region bounded by the line y = mx (m > 0), the x-axis and the lines x = 1 and x = 2 is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{3m}{2}\)
Since m > 0, the line y = mx lies above the x-axis for \(1 \le x \le 2\), so the area is the integral of y itself:
\( \displaystyle A = \int_{1}^{2} mx\,dx \)
\( \displaystyle = m\left[\frac{x^{2}}{2}\right]_{1}^{2} \)
\( \displaystyle = m\left(2-\frac{1}{2}\right) = \frac{3m}{2} \)