### Home > APCALC > Chapter 1 > Lesson 1.1.1 > Problem1-5

1-5.

Sketch the function $g(x) =\sqrt { 16 - x ^ { 2 } }$ .

You should recognize this function as a semicircle with radius $4$, centered at the origin.

1. State the domain and range of $g$

2. Use geometry to calculate the area under the curve for $0 ≤ x ≤ 4$.

$\text{On the graph of }g(x),\text{ shade the region }A(g,0\le x\le4).\text{ Observe that this area is }\frac{1}{4}\text{ the area of a }$
$\text{ complete circle, and }\frac{1}{2}\text{ the area of the semicircle, }g(x).$

$\text{Area of a quarter-circle }=\frac{1}{4}\pi r^2$

1. Now calculate the area under the curve for $–4 ≤ x ≤ 4$.