For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F and the boundary surface S . For each closed surface, assume N is the outward unit normal vector. 380. [T] F ( x , y , z ) = x 2 i + y 2 j + z 2 k ; S is the surface of sphere x 2 + y 2 + z 2 = 4 .
For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F and the boundary surface S . For each closed surface, assume N is the outward unit normal vector. 380. [T] F ( x , y , z ) = x 2 i + y 2 j + z 2 k ; S is the surface of sphere x 2 + y 2 + z 2 = 4 .
For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral
∫
s
F
⋅
n
d
S
for the given choice of F and the boundary surface S. For each closed surface, assume N is the outward unit normal vector.
380. [T]
F
(
x
,
y
,
z
)
=
x
2
i
+
y
2
j
+
z
2
k
; S is the surface of sphere
x
2
+
y
2
+
z
2
=
4
.
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.
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