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Mathematics
Problem
For a particle that moves along a line with velocity
v
(
t
)
v(t)
v
(
t
)
on the interval
[
a
,
b
]
[a,b]
[
a
,
b
]
, which of the following integrals represents the total distance traveled during that interval? a)
1
2
∫
a
b
∣
v
(
t
)
∣
d
t
\displaystyle \tfrac12\int_a^b |v(t)|\,dt
2
1
∫
a
b
∣
v
(
t
)
∣
d
t
b)
∫
a
b
∣
v
(
t
)
∣
d
t
\displaystyle \int_a^b |v(t)|\,dt
∫
a
b
∣
v
(
t
)
∣
d
t
c)
∫
a
b
v
(
t
)
d
t
\displaystyle \int_a^b v(t)\,dt
∫
a
b
v
(
t
)
d
t
d)
∣
∫
a
b
v
(
t
)
d
t
∣
\displaystyle \left|\int_a^b v(t)\,dt\right|
∫
a
b
v
(
t
)
d
t
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