Use Stokes’s Theorem to evaluate ∮ C F . d r . F( x , y , z ) = z 2 i + 2 x j − y 3 k; C is the circle x 2 + y 2 = 1 in the xy - plane with counterclockwise orientation looking down the positive z -axis.
Use Stokes’s Theorem to evaluate ∮ C F . d r . F( x , y , z ) = z 2 i + 2 x j − y 3 k; C is the circle x 2 + y 2 = 1 in the xy - plane with counterclockwise orientation looking down the positive z -axis.
F(
x
,
y
,
z
)
=
z
2
i
+
2
x
j
−
y
3
k;
C
is the circle
x
2
+
y
2
=
1
in the xy-plane with counterclockwise orientation looking down the positive z-axis.
Evaluate
| 2*(x + 7) – 2y ds
where C is the circle of radius 1 centered at (-3,0) and lying on the plane x = -3.
Evaluate ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9 with positive direction using Green's Theorem.
Find
F. dr where C is a circle of radius 3 in the plane x + y + z = 4, centered at (3, 3, -2) and oriented clockwise when viewed from the origin, if
F= 4yi 3x]+(y − x)k
-
Sc F.dr =
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