Volumes by Integration: Shell Method Practice Problem Solution
3. Take the area bounded by the x axis and y=5x-x2-4 and rotate it about the y axis and determine the volume.
Here is the volume. It’s sort of a half-bagel shape.
Then write the equation for dV=2pr*height*thickness
dV=2p(5x-x2-4)xdx
Now set limits and integrate. To set the limits, we have to determine where the curve intersects the x axis first.
Set y = 5x-x2-4=0 and solve. We get x=1, 4. These are the limits.
