Mathematics - Area Under Curves Question with Solution | TestHub

The given lines are $y=2x$, $y=\frac{x}{2}$, and $x=2$.

The points of intersection of the lines are $(0,0)$, $(2,4)$, and $(2,1)$.

The region is bounded by the upper line $y=2x$ and the lower line $y=\frac{x}{2}$ from $x=0$ to $x=2$.

The area of the region is given by the integral of the difference between the upper and lower curves:

$\text{Area}={\int }_0^2\left(2x-\frac{x}{2}\right)dx$

$\text{Area}={\int }_0^2\frac{3x}{2}dx$

$\text{Area}={\left[\frac{3x^2}{4}\right]}_0^2$

$\text{Area}=\frac{3(2{)}^2}{4}-0=3$

Answer: $3$