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.
please make sure this is right calc3
make sure its right
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Question Help: Message instructor
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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