Surface integrals using a parametric description Evaluate the surface integral ∬ S f ( x , y , z ) d S using a parametric description of the surface . 29. f ( x , y , z ) = x , where S is the cylinder x 2 + z 2 = 1 , 0 ≤ y ≤ 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 . 29. f ( x , y , z ) = x , where S is the cylinder x 2 + z 2 = 1 , 0 ≤ y ≤ 3
Surface integrals using a parametric descriptionEvaluate the surface integral
∬
S
f
(
x
,
y
,
z
)
d
S
using a parametric description of the surface.
29.
f
(
x
,
y
,
z
)
=
x
, where S is the cylinder
x
2
+
z
2
=
1
,
0
≤
y
≤
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.
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
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.)
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.)
Chapter 17 Solutions
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Thomas' Calculus: Early Transcendentals (14th Edition)
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