### 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 $g$

Consider the radius and center of the semicircle. This should help you determine domain and range?

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 $–4 ≤ x ≤ 4$.

You can use your answer to part (b) and help answer part (c).

1. What is the relationship between the answers to parts (b) and (c)?

The area in (c) is double the area in (b). Be sure to confirm this numerically.