Applications of Double Integrals

Area?

Total mass?

Integrating mass-density function gives you mass

NOTE:
IF a region has constant density at every point, then mass = density function * area

First moment about x-axis?

Y times mass-density function dA

First moment about y-axis?

X-pose Center of Mass?

Y-pose of Center of Mass?

Second Moment (moment of inertia) about
x-axis

Second Moment (moment of inertia) about
y-axis

Second moment (moment of inertia) about origin?

Parallel Axis Theorem

TRIPLE INTEGRAL
Mass?

integrate mass-density function

First moment with respect to YZ

First moment w/r/t xz

First moment w/r/t xy

center of mass w/r/t x

CoM w/r/t y

CoM z-coord

moment of inertia Ix

Moment of inertia Iy

Iz