University Mathematics Handbook (2015)

VIII. Integral Calculus of Multivariable Functions

Chapter 5. Geometric and Physical Applications

a.  Area of Domain :

b.  The volume of a cylindrical solid bounded by a cylindrical surface the directrix of which is parallel to -axis and bounded above by surface and below by is

when is the projection of the body on plane .

c.  Mass of planar body with planar density

d.  The static moment of inertia of planar region , with planar density

1.  Relative to -axis

2.  Relative to -axis