How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=f(x)=3x-x^2# and x axis revolved about the x=-1?
Imagine a cylindrical shell as a rectangular prism with width
The volume of the cylindrical shell is width x length x thickness (height)
If we sketch the parabola
Also, the radius of the cylindrical shell is considered to be the distance from the axis of revolution
i.e. the change in volume,
To find the volume, we limit the thickness of the shells, and find their summation within the domain