Volumes by Integration

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


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.