9.13 Surface Integrals

1
9.13 Surface Integrals
Arclength
2
Surface Area
Def Surface Area
3
9.13 Surface Integrals
Example
Find the surface area of that portion of the
plane z6-3x-2y that is bounded by the
coordinate planes in the first octant
4
Ex 1/ pp 527
Find the surface area of that portion of the
plane 2x 3y 4z 12 that is bounded by the
coordinate planes in the first octant
5
surface Integral
Differential of surface Area
6
EX 15,19 / pp 527
MATLAB ezsurf('2-x2',-4,4)
7
EX 15,19 / pp 527
8
Mass of a surface
9
Orientable Surface
In Example 5, Surface Integral of a vector field
We need the concept of orientable surface
Def (Roughly) orientable surface S has two sides
that could be painted different colors.
Example (Mobius Strip) Not an orientable surface
10
(Mobius Strip)
1)Cut on the middle 2)Cut on 1/3
11
(No Transcript)
12

• Def
• A smooth surface S is orientable if there exists
  a cont unit normal vector n defined at each point
  (x,y,z) on the surface.
• The vector field n(x,y,z) is called the
  orientation of S
• S has two orientations n(x,y,z) and -n(x,y,z)
• Upward ( k component) and downward (-k
  component)