Disc Method - Rotation about the Washer Method - Rotation about Cylindrical Shell Method: Volume of the x-axis: Disc Method: Revolution Cylinder Method - Rotation about the y-axis: Moments of NA NA (see Wikipedia) Inertia 3-D for Continuous: 2-D for Discrete: 3-D for Discrete: where Center of Mass Where is distance from 1-D for Discrete: where the axis of rotation, not and origin. Gradient where Line Integral NA NA where Surface NA NA Integral and
Volume of Revolution Disc Method - Rotation about the Washer Method - Rotation about the x-axis: Cylinder Method - Rotation about the y-axis: Disc Method: Cylindrical Shell Method: Moments of Inertia NA NA (see Wikipedia) Center of Mass where 1-D for Discrete: 2-D for Discrete: 3-D for Discrete: 3-D for Continuous: where and Where is distance from the axis of rotation, not origin. Gradient where Line Integral NA NA Surface Integral where and NA NA
Harolds_Calculus_3_Cheat_Sheet_2017.docx