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.
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.
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Find the surface area of the "Coolio McSchoolio" surface shown below using the formula:
SA = integral, integral D, ||ru * rv||dA
%3D
The parameterization of the surface is:
r(u,v) = vector brackets (uv, u + v, u - v) where u^2 + v^2 <= 1
A.) (pi/3)(6squareroot(6) - 8)
B.) (pi/3)(6squareroot(6) - 2squareroot(2))
C.) (pi/6)(2squareroot(3) - squareroot(2))
D.) (pi/6)(squareroot(6) - squareroot(2))
E.) (5pi/6)(6 - squareroot(2))
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)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus Enhanced with Graphing Utilities
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