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Mathematics
Mathematics
Problem
For a particle moving along a straight line with velocity
v
(
t
)
v(t)
v
(
t
)
, which of the following definite integrals gives the particle’s total distance traveled from
t
=
a
t=a
t
=
a
to
t
=
b
t=b
t
=
b
? a)
∣
∫
a
b
v
(
t
)
d
t
∣
\displaystyle \left|\int_{a}^{b} v(t)\,dt\right|
∫
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 \int_{a}^{b} |v(t)|\,dt
∫
a
b
∣
v
(
t
)
∣
d
t
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