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. 331. F ( x , y , z ) = 2 y i − 6 z j + 3 x k ; S is a portion of paraboloid z = 4 − x 2 − y 2 and is above the x y -plane.
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. 331. F ( x , y , z ) = 2 y i − 6 z j + 3 x k ; S is a portion of paraboloid z = 4 − x 2 − y 2 and is above the x y -plane.
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.
331.
F
(
x
,
y
,
z
)
=
2
y
i
−
6
z
j
+
3
x
k
;
S
is a portion of paraboloid
z
=
4
−
x
2
−
y
2
and is above the
x
y
-plane.
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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