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

The correct option is B $4$

Area bounded by the lines $y=mx,x=1,x=2$ and the x-axis is given by,

$|{\int }_1^2\left(mx\right)dx|=\left|m{\int }_1^{2}xdx\right|=\left|m{\left[\frac{x^2}{2}\right]}_1^2\right|=6$ (given in the question)

$\Rightarrow |m(2-\frac{1}{2})|=6$

$\Rightarrow |m|=4\therefore m=4$ or $m=-4$ So the answer is $m=4$ as given in the options.