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 141. [T] Let C: [ 1, 2] → ℝ 2 be given by x = e t − 1 , y = sin ( π t ) . Use a computer to compute the integral ∫ c F . d s = ∫ c 2 x cos y d x − x 2 sin y d y , where F = ( 2 x cos y ) i − ( x 2 sin y ) j .
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 141. [T] Let C: [ 1, 2] → ℝ 2 be given by x = e t − 1 , y = sin ( π t ) . Use a computer to compute the integral ∫ c F . d s = ∫ c 2 x cos y d x − x 2 sin y d y , where F = ( 2 x cos y ) i − ( x 2 sin y ) j .
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
141. [T] Let C: [1, 2]
→
ℝ
2
be given by
x
=
e
t
−
1
,
y
=
sin
(
π
t
)
.
Use a computer to compute the integral
∫
c
F
.
d
s
=
∫
c
2
x
cos
y
d
x
−
x
2
sin
y
d
y
,
where
F
=
(
2
x
cos
y
)
i
−
(
x
2
sin
y
)
j
.
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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