(Solved): Use the Shell Method to compute the volume obtained by rotating the region enclosed by the graphs ...

Use the Shell Method to compute the volume obtained by rotating the region enclosed by the graphs as indicated, about the \( y \)-axis. \[ y=3 x-2, y=6-x, x=0 \] (Use symbolic notation and fractions where needed.) \[ V= \] \[ y=8-x^{3}, \quad y=8-4 x \] (Use symbolic notation and fractions where needed.) \[ V \] Use the Shell Method to compute the volume obtained by rotating the region enclosed by the graphs as indicated, about the \( y \) axis. \[ y=\left(x^{2}+1\right)^{-2}, y=2-\left(x^{2}+1\right)^{-2}, x=6 \] (Use symbolic notation and fractions where needed.) \[ V= \] Using the Shell Method, find the volume of the solid obtained by rotating the region underneath the graph of \( f \) over the given interval about the line \( x=2 \). \[ f(x)=x^{3}, \quad[0,1] \] (Use symbol notation and fractions where needed.) volume: