Mathematics - Area Under Curves Question with Solution | TestHub

The given curves are $y=|x|$ and $y=4-|x|$.

To find the points of intersection, we equate the two equations:

$|x|=4-|x|$

$2|x|=4\Rightarrow |x|=2\Rightarrow x=\pm 2$

The required area is bounded between $x=-2$ and $x=2$. Since both functions are even, the area is symmetric about the y-axis.

Area $={\int }_{-2}^2((4-|x|)-|x|)dx$

Area $=2{\int }_0^2(4-2x)dx$

Area $=2{\left[4x-x^2\right]}_0^2$

Area $=2(8-4)=8$ sq units.

Answer: $8$