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Mathematics
Problem
A particle moves in the plane with velocity vector
v
(
t
)
=
⟨
a
(
t
)
,
b
(
t
)
⟩
\mathbf v(t)=\langle a(t),b(t)\rangle
v
(
t
)
=
⟨
a
(
t
)
,
b
(
t
)⟩
. Explain how the definite integral of
v
(
t
)
\mathbf v(t)
v
(
t
)
on an interval
[
p
,
q
]
[p,q]
[
p
,
q
]
is related to the particle’s change in position over that same interval.
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