Surface integrals using an explicit description Evaluate the surface integral ∬ S f ( x , y , z ) d S using an explicit representation of the surface . 37. f ( x , y , z ) = 25 − x 2 − y 2 ; S is the hemisphere centered at the origin with radius 5, for z ≥ 0.
Surface integrals using an explicit description Evaluate the surface integral ∬ S f ( x , y , z ) d S using an explicit representation of the surface . 37. f ( x , y , z ) = 25 − x 2 − y 2 ; S is the hemisphere centered at the origin with radius 5, for z ≥ 0.
Surface integrals using an explicit descriptionEvaluate the surface integral
∬
S
f
(
x
,
y
,
z
)
d
S
using an explicit representation of the surface.
37.
f
(
x
,
y
,
z
)
=
25
−
x
2
−
y
2
; S is the hemisphere centered at the origin with radius 5, for z ≥ 0.
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.
Fine the area of the surface obtained by the rotating the following curve about the x-axis. (The interval is provided in the image.)
Firnd the area of the surface of the half cylinder {(r,0,z): r=6, 0s0S1, 0SzS5} using a parametric description of the surface.
Set up the integral for the surface area using the parameterization u=0 and v=z.
!!
S SO du dv
(Type an exact answers, using x as needed.)
The surface area is
(Type an exact answer, using x as needed.)
Evaluate the surface integral SG(x,y,z) do using a parametric description of the surface.
S
G(x,y,z) = z², over the hemisphere x² + y² + z² = 4, zz0
The value of the surface integral is.
(Type an exact answer, using as needed.)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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