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

1. State the domain and range of $g$. 

   Hint (a):

   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 $0 ≤ x ≤ 4$.

   Hint (b):

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

   More Help (b):

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

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

   Hint (c):

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

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

   Answer (d):

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