A hint to get started
Rotate a below-axis region through a full turn
Find the value of the volume of the solid generated by rotating the region bounded by and the x-axis through four right angles about the x-axis.
CJC · Lecture · Example 14
The Teacher circles four right-angles, marks the x-axis and fills the squared-function integral and 3.83 to 3 sf. These additions are integrated into the first two steps and answer.
Below-axis heights still produce positive radii and volume; squaring removes the sign. The exact evaluation here is independently authored.