Consider the function $$f ( x ) = \begin{cases} | 5 x ( x + 2 ) | & ( x < 0 ) \\ | 5 x ( x - 2 ) | & ( x \geq 0 ) \end{cases}$$ On the closed interval $[ 0,1 ]$, what is the volume of the solid of revolution generated by rotating the region enclosed by the graph of $y = f ( x )$, the $x$-axis, and the line $x = 1$ about the $x$-axis? [3 points] (1) $\frac { 65 } { 6 } \pi$ (2) $\frac { 35 } { 3 } \pi$ (3) $\frac { 25 } { 2 } \pi$ (4) $\frac { 40 } { 3 } \pi$ (5) $\frac { 85 } { 6 } \pi$
Consider the function
$$f ( x ) = \begin{cases} | 5 x ( x + 2 ) | & ( x < 0 ) \\ | 5 x ( x - 2 ) | & ( x \geq 0 ) \end{cases}$$
On the closed interval $[ 0,1 ]$, what is the volume of the solid of revolution generated by rotating the region enclosed by the graph of $y = f ( x )$, the $x$-axis, and the line $x = 1$ about the $x$-axis? [3 points]\\
(1) $\frac { 65 } { 6 } \pi$\\
(2) $\frac { 35 } { 3 } \pi$\\
(3) $\frac { 25 } { 2 } \pi$\\
(4) $\frac { 40 } { 3 } \pi$\\
(5) $\frac { 85 } { 6 } \pi$