For the following exercises, show that the following vector fields ate conservative by using a computer. Calculate ∫ c F . d r for the given curve. 137. F = 2 x y 2 + 1 i − 2 y ( x 2 + 1 ) ( y 2 + 1 ) 2 j ; C is Parameterized by x = t 3 − 1 , y = t 6 − t , 0 ≤ t ≤ 1
For the following exercises, show that the following vector fields ate conservative by using a computer. Calculate ∫ c F . d r for the given curve. 137. F = 2 x y 2 + 1 i − 2 y ( x 2 + 1 ) ( y 2 + 1 ) 2 j ; C is Parameterized by x = t 3 − 1 , y = t 6 − t , 0 ≤ t ≤ 1
For the following exercises, show that the following vector fields ate conservative by using a computer. Calculate
∫
c
F
.
d
r
for the given curve.
137.
F
=
2
x
y
2
+
1
i
−
2
y
(
x
2
+
1
)
(
y
2
+
1
)
2
j
;
C is Parameterized by
x
=
t
3
−
1
,
y
=
t
6
−
t
,
0
≤
t
≤
1
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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