Area by Parts and Rotational Volume
Disk Method
Disk method: the concept is adding an infinite number of disks to get an area.
For a rotation around the x axis the formula is 
For example:
2.1 Find the volume from rotating the function 
about the x axis from x = 0 to 9.
For a rotation around the y axis the formula is 
For example:
2.2 Find the volume from rotating the function y = 3x about the y axis from y = 0 to 6.
Check this with the formula for the area of a cone. Area of a cone = 
Area of this cone = 
2.3 Find the volume from rotating the function 
about the x axis from 
is symmetric to the y axis so 
or the formula for the area of a sphere.
