Surface integrals using an explicit description Evaluate the surface integral ∬ S f ( x , y , z ) d S using an explicit representation of the surface . 38. f ( x , y , z ) = e z ; S is the plane z = 8 – x – 2 y in the first octant.
Surface integrals using an explicit description Evaluate the surface integral ∬ S f ( x , y , z ) d S using an explicit representation of the surface . 38. f ( x , y , z ) = e z ; S is the plane z = 8 – x – 2 y in the first octant.
Solution Summary: The author explains the surface integral displaystyleundersetSiintf(x,y,z)dS with the help of explicit description.
Surface integrals using an explicit descriptionEvaluate the surface integral
∬
S
f
(
x
,
y
,
z
)
d
S
using an explicit representation of the surface.
38.
f
(
x
,
y
,
z
)
=
e
z
; S is the plane z = 8 – x – 2y in the first octant.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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))
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.
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