Question

The area of the region bounded by the lines $y=mx,x=1,x=2,$ and $x$ axis is $6$ sq. units, then $m$ is

• A. 1
• B. 4
• C. 3
• D. 2

Answer 1

Answer: (B)

Given, equation of line is $y=mx$ and bounded by $x=1,x=2$ and $x$ -axis

$\therefore$ Required area $=\underset{1}{\overset{2}{\int }}mxdx$
$\Rightarrow 6=m{\left[\frac{x^2}{2}\right]}_1^2$
$\Rightarrow 6=m\left(\frac{4}{2}-\frac{1}{2}\right)$
$\Rightarrow 6=m\times \frac{3}{2}$
$\Rightarrow m=4$