Question

The area of the region bounded by the lines$\mathrm{y}=\mathrm{mx},\mathrm{x}=1,\mathrm{x}=2$ and $\mathrm{x}$-axis is $6$ sq units, then $\mathrm{m}$ is equal to:

• A. $3$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is D

$4$

Explanation for correct option

Calculating the value of m$m$

Given, the curves are: $\mathrm{y}=\mathrm{mx},\mathrm{x}=1,\mathrm{x}=2$

Area of the region bounded by the curves is $6\mathrm{sq}\mathrm{units}$.

Visualizing the three curves on a graph paper we get:

Area of the bounded region is given by:

$$\begin{gathered} \mathrm{A}={\int }_1^2\mathrm{mxdx} \\ \Rightarrow \mathrm{A}={\left[\frac{{\mathrm{mx}}^2}{2}\right]}_1^2 \\ \Rightarrow 6=\left[\frac{\mathrm{m}}{2}\times 4-\frac{\mathrm{m}}{2}\right]\left[\mathrm{Given}\right] \\ \Rightarrow 6=2\mathrm{m}-\frac{\mathrm{m}}{2} \\ ⟹12=3\mathrm{m} \\ \therefore \mathrm{m}=4 \end{gathered}$$

Hence, the correct answer is Option (D).