Surface integrals using a parametric description Evaluate the surface integral ∬ S f ( x , y , z ) d S using a parametric description of the surface . 27. f ( x , y , z ) = x 2 + y 2 , where S is the hemisphere x 2 + y 2 + z 2 = 36 , for z ≥ 0
Surface integrals using a parametric description Evaluate the surface integral ∬ S f ( x , y , z ) d S using a parametric description of the surface . 27. f ( x , y , z ) = x 2 + y 2 , where S is the hemisphere x 2 + y 2 + z 2 = 36 , for z ≥ 0
Surface integrals using a parametric descriptionEvaluate the surface integral
∬
S
f
(
x
,
y
,
z
)
d
S
using a parametric description of the surface.
27.
f
(
x
,
y
,
z
)
=
x
2
+
y
2
, where S is the hemisphere
x
2
+
y
2
+
z
2
=
36
, for z ≥ 0
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.
Find the area of the surface.
The surface with parametric equations x = u?, y = uv, z = v², o s u s 2, 0 < v < 3.
2
Surface area of an ellipsoid Consider the ellipsoidx2/a2 + y2/b2 + z2/c2 = 1, where a, b, and c are positive real numbers.a. Show that the surface is described by the parametric equations r(u, ν) = ⟨a cos u sin ν, b sin u sin ν, c cos ν⟩ for 0 ≤ u ≤ 2π, 0 ≤ ν ≤ π.b. Write an integral for the surface area of the ellipsoid.
Parameterize the portion of the surface f(x, y)
octant, bounded by the planes a = 0, y = 0, x + y = 1. Include a
xy in the first
sketch (hand-drawn or Maple-rendered) of just this portion of the
surface.
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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