Question

The area of region bounded by the lines $y=mx,x=1$ and $x=2$ and the x-axis is $7.5sq.units$, then $m$ is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (D)

$5$

The area bounded by the lines $y=mx,x=1,x=2$ and $x$-axis is given by $A={\int }_1^{2}ydx$.

Given $A=7.5$

Thus ${\int }_1^{2}ydx=7.5$

$\Rightarrow {\int }_1^{2}mxdx=7.5$

$\Rightarrow {\left[\frac{m{x}^2}{2}\right]}_1^2=7.5$

$\Rightarrow \frac{4m}{2}-\frac{m}{2}=7.5$

$\Rightarrow \frac{3m}{2}=7.5$

$\Rightarrow 3m=15$

$\Rightarrow m=\frac{15}{3}$

$\therefore m=5$