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Undergraduate
Calculus
Calculus Of Variations
Recall that the work required to move an object along a curve
Undergraduate
Recall that the work required to move an object along a curve C in a force field F is given by W = C F
Recall that the work required to move an object along a curve C in a force field F is given by
W
=
C
F
dr
=
ba
F
(
r
(
t
)
)
r
'
(
t
)
dt
,
where
r
(
t
)
,
a
t
b
,
is a parameterization of C
.
A simple way to parameterize the given curve C is to let
x
=
x
(
t
)
=
t
,
and rewrite
y
=
x
3
in terms of t
.
y
=
y
(
t
)
=
t
3
With this parameterization, the part of the curve from
(
0
,
0
)
to
(
2
,
8
)
corresponds to an initial value
t
=
a
=
and terminal value
t
=
b
=
.
Step by Step Solution
1
Understanding Responsive Design Principles
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