True or False ? Justify your answer with a proof or a counterexample. 428. For vector field F ( x , y ) = P ( x , y ) i + Q ( x , y ) j , if P y ( x , y ) = Q x ( x , y ) in open region D , then ∫ ∂ D P d x + Q d y = 0 .
True or False ? Justify your answer with a proof or a counterexample. 428. For vector field F ( x , y ) = P ( x , y ) i + Q ( x , y ) j , if P y ( x , y ) = Q x ( x , y ) in open region D , then ∫ ∂ D P d x + Q d y = 0 .
True or False? Justify your answer with a proof or a counterexample.
428. For vector field
F
(
x
,
y
)
=
P
(
x
,
y
)
i
+
Q
(
x
,
y
)
j
, if
P
y
(
x
,
y
)
=
Q
x
(
x
,
y
)
in open region
D
, then
∫
∂
D
P
d
x
+
Q
d
y
=
0
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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