Multiple Choice: Which integral below calculates the volume generated when the region bounded by $f(x)$ and $g(x)$ (shown at right) is rotated about the $y$-axis?

1. $2 \pi \int _ { 1 } ^ { 4 } x ( f ( x ) - g ( x ) ) d x$

2. $2 \pi \int _ { 1 } ^ { 4 } x ( g ( x ) - f ( x ) ) d x$

3. $\pi \int _ { 1 } ^ { 4 } ( f ( x ) - g ( x ) ) ^ { 2 } d x$

4. $\pi \int _ { 1 } ^ { 4 } ( g ^ { 2 } ( x ) - f ^ { 2 } ( x ) ) d x$

5. None of these