The area bounded by semi circle $\mathrm{y}=\sqrt{4-{\mathrm{x}}^2}$and its diameter y = 0 is

The area between the semicircle and the x-axis from -2 to 2 can be computed using the geometry formula

$\text{ Area }=\frac{1}{2}\cdot \pi r^2=\frac{1}{2}\cdot \pi (2{)}^2=2\pi$

$\text{ Because }f\text{ is nonnegative, the area is also the value of the integral of }f\text{ from }-2\text{ to }2\text{, }$

${\int }_{-2}^2 \sqrt{4-x^2}dx=2\pi$