On graph paper, sketch the function $g ( x ) = \sqrt { 36 - x ^ { 2 } }$. Shade the area under the curve for $3 ≤ x ≤ 6$. .

1. Use geometry to calculate this area. Hint: Draw in a radius to create two easier regions whose difference is the shaded region.

   Hint (a):

   You should recognize $g$ as the equation of a semicircle, centered at the origin, with radius $6$.

   More Help(a):

   View the eTool. The height of the triangle is $5$ and the hypotenuse is $6$. Use these lengths to calculate the measure of the central angle.

2. Calculate the area under the curve for $0 ≤ x ≤ 3$.

3. Calculate the area under the curve for $–3 ≤ x ≤ 6$.