CPM Homework Help : CALC Problem 1-86

A flag is defined by the region between the $x$ -axis and:

$f ( x ) = \left\{ \begin{array} { r } { - x + 5 \text { for } 1 \leq x \leq 3 } \\ { 2 \quad \text { for } 3 < x \leq 6 } \end{array} \right.$

Find the volume generated when the flag is rotated about the $x$ -axis. .

Hint 1:

Sketch the flag. Since we do not know a geometric formula for the 3D figure that this flag will generate, subdivide it into familiar 3-D shapes:

Hint 2:

What 3-D shapes will this generate? You should identify three.

Hint 3:

a big cone $−$ a small cone $+$ a cylinder

Use the eTool below to view the graph.
Click the link at right for the full version of the eTool: Calc 1-86 HW eTool