Surface integrals using a parametric description Evaluate the surface integral ∬ S f ( x , y , z ) d S using a parametric description of the surface . 30. f ( ρ , φ , θ ) = cos φ , where S is the part of the unit sphere in the first octant
Surface integrals using a parametric description Evaluate the surface integral ∬ S f ( x , y , z ) d S using a parametric description of the surface . 30. f ( ρ , φ , θ ) = cos φ , where S is the part of the unit sphere in the first octant
Solution Summary: The author evaluates the surface integral of f over the smooth surface S. The parametric description of the sphere is r(u,v)=langle
Surface integrals using a parametric descriptionEvaluate the surface integral
∬
S
f
(
x
,
y
,
z
)
d
S
using a parametric description of the surface.
30.
f
(
ρ
,
φ
,
θ
)
=
cos
φ
, where S is the part of the unit sphere in the first octant
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.
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.
Identify the surface Describe the surface with the given parametric representation.
r(u, v) = ⟨v, 6 cos u, 6 sin u⟩ , for 0 ≤ u ≤ 2π, 0 ≤ v ≤ 2
The equation of the tangent plane to the surface defined by z = y exp(-r) at the point (0, 1, 1) is
= Z
Preview My Answers
Submit Answers
Chapter 17 Solutions
Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.