(Solved): Set up the integral that gives the volume of the solid formed by revolving the region bounded by \( ...

Set up the integral that gives the volume of the solid formed by revolving the region bounded by \( y=7 \) and \( y=14-\frac{x^{2}}{14} \) about the \( x \)-axis. \[ V=\pi \int_{-7 \sqrt{2}}^{7 \sqrt{2}}\left(\left(14-\frac{x^{2}}{14}\right)^{2}-49\right) d x \] \[ V=2 \pi \int_{-7 \sqrt{2}}^{7 \sqrt{2}} x\left(14-\frac{x^{2}}{14}-49\right) d x \] \[ V=\pi \int_{-14}^{14}\left(\left(14-\frac{x^{2}}{14}\right)^{2}-49\right) d x \] \[ V=2 \pi \int_{-14}^{14} x\left(14-\frac{x^{2}}{14}-49\right) d x \] None of these