CPM Homework Help : CALC Problem 1-54

On graph paper, sketch the function $g ( x ) = \sqrt { 36 - x ^ { 2 } }$ . Shade $A(g, 3 ≤ x ≤ 6)$ , the region between $g(x)$ and the $x$ -axis, for $3 ≤ x ≤ 6$ . .

Use geometry to find this area. Hint: Draw in a radius to create two easier regions whose difference is the shaded region.
Find $A(g, 0 ≤ x ≤ 3)$ .
Find $A(g, -3 ≤ x ≤ 6)$ .

Hint:

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

Use the eTool below for parts (a) - (c).
Click the link at right for the full version of the eTool: Calc 1-54 HW eTool