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  4. 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

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Q. 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

KCETKCET 2014Application of Integrals

Solution:

Given, equation of line is $y=m x$ and bounded by $x=1, x=2$ and $x$ -axis
image
$\therefore $ Required area $=\int\limits_{1}^{2} m x dx$
$\Rightarrow 6=m\left[\frac{x^{2}}{2}\right]_{1}^{2}$
$\Rightarrow 6= m\left(\frac{4}{2}-\frac{1}{2}\right)$
$\Rightarrow 6=m \times \frac{3}{2}$
$\Rightarrow m=4$