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Mathematics
Problem
Describe the difference in physical meaning between the definite integral
∫
a
b
v
(
t
)
d
t
\displaystyle\int_a^b v(t)\,dt
∫
a
b
v
(
t
)
d
t
and the definite integral
∫
a
b
∣
v
(
t
)
∣
d
t
\displaystyle\int_a^b |v(t)|\,dt
∫
a
b
∣
v
(
t
)
∣
d
t
for a particle moving along a line with velocity
v
(
t
)
v(t)
v
(
t
)
.
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