Surface integrals using a parametric description Evaluate the surface integral ∬ S f ( x , y , z ) d S using a parametric description of the surface . 28 . f ( x , y , z ) = y , where S is the cylinder x 2 + y 2 = 9 , 0 ≤ z ≤ 3
Surface integrals using a parametric description Evaluate the surface integral ∬ S f ( x , y , z ) d S using a parametric description of the surface . 28 . f ( x , y , z ) = y , where S is the cylinder x 2 + y 2 = 9 , 0 ≤ z ≤ 3
Surface integrals using a parametric descriptionEvaluate the surface integral
∬
S
f
(
x
,
y
,
z
)
d
S
using a parametric description of the surface.
28.
f
(
x
,
y
,
z
)
=
y
, where S is the cylinder
x
2
+
y
2
=
9
,
0
≤
z
≤
3
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Evaluate the surface integral G(x,y,z) do using a parametric description of the surface.
S
2
2
G(x,y,z) = 3z², over the hemisphere x² + y² +22² = 4, zz0
The value of the surface integral is
(Type an exact answer, using it as needed.)
Firnd the area of the surface of the half cylinder {(r,0,z): r=6, 0s0S1, 0SzS5} using a parametric description of the surface.
Set up the integral for the surface area using the parameterization u=0 and v=z.
!!
S SO du dv
(Type an exact answers, using x as needed.)
The surface area is
(Type an exact answer, using x as needed.)
y?
For function f (x, y)
x2+1
In the three dimensional space consider a surface z =
f (x, y)
Find parametric equations for the normal line to the surface at the
point (1, 2, f(1, 2))
A x = 1- 2t, y = 2 + 2t, z = 2 – t
x = 1+ 2t, Y = 2 + 2t, z = 2+t
C a = 1-t, y = 2 + t, z = 2 – t
%3D
Chapter 14 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
Precalculus Enhanced with Graphing Utilities (7th Edition)
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