Transcription of Contiune on 16.7 Triple Integrals - University of Notre Dame
{{id}} {{{paragraph}}}
Example: confidence
Contiune on 16.7 Triple Integrals - University of Notre Dame
Contiune on Triple Integrals Figure 1: ZZZ Z Z "Z u2 (x,y). #. f (x, y, z)dV = f (x, y, z)dz dA. E D u1 (x,y). Applications of Triple Integrals Let E be a solid region with a density function (x, y, z). RRR. Volume: V (E) = E. 1dV. RRR. Mass: m = E. (x, y, z)dV. Moments about the coordinate planes: ZZZ. Mxy = z (x, y, z)dV. E. ZZZ. Mxz = y (x, y, z)dV. E. ZZZ. Myz = x (x, y, z)dV. E. Center of mass: (x , y , z ). x = Myz /m , y = Mxz /m , z = Mxy /m . Remark: The center of mass is just the weighted average of the coordinate functions over the solid region. If (x, y, z) = 1, the mass of the solid equals its volume and the center of mass is also called the centroid of the solid.
A point in space can be located by using polar coordinates r,θ in the xy-plane and z in the vertical direction. Some equations in cylindrical coordinates (plug in x = rcos(θ),y = rsin(θ)):
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: