Find the volume of the solid generated by revolving the region bounded by the given line and curve about the \( x \)-axis. \( y=\sqrt{64-x^{2}}, y=0 \) Set up the integral that gives the volume of the solid.

To find the volume of the solid generated by revolving the region bounded by the curve \( y = \sqrt{64 - x^2} \) and the line \( y = 0 \) about the \( x \)-axis, we first recognize that the curve represents a semicircle with radius \( 8 \) centered at the origin. The volume \( V \) can be calculated using the disk method: \[ V = \pi \int_{-8}^{8} \left( \sqrt{64 - x^2} \right)^2 \, dx \] This simplifies to: \[ V = \pi \int_{-8}^{8} (64 - x^2) \, dx \] The limits of integration \(-8\) to \(8\) correspond to the \(x\)-intercepts of the semicircle. Now you have everything you need to set up the integral for the volume!