For the following exercises, without using Stokes’ theorem, calculate directly both the flux of curl F ⋅ N over the given surface and the circulation integral around its boundary, assuming all boundaries are oriented clockwise as viewed from above. 329. F ( x , y , z ) = z i + 2 x j + 3 y k ; S is upper hemisphere z = 9 − x 2 − y 2 .
For the following exercises, without using Stokes’ theorem, calculate directly both the flux of curl F ⋅ N over the given surface and the circulation integral around its boundary, assuming all boundaries are oriented clockwise as viewed from above. 329. F ( x , y , z ) = z i + 2 x j + 3 y k ; S is upper hemisphere z = 9 − x 2 − y 2 .
For the following exercises, without using Stokes’ theorem, calculate directly both the flux of curl
F
⋅
N
over the given surface and the circulation integral around its boundary, assuming all boundaries are oriented clockwise as viewed from above.
329.
F
(
x
,
y
,
z
)
=
z
i
+
2
x
j
+
3
y
k
;
S
is upper hemisphere
z
=
9
−
x
2
−
y
2
.
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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