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Mathematics
Problem
Which of the following expressions represents the total distance traveled (in meters) by a particle with velocity
v
(
t
)
=
t
2
−
4
t
+
3
v(t)=t^{2}-4t+3
v
(
t
)
=
t
2
−
4
t
+
3
m/s from
t
=
0
t=0
t
=
0
to
t
=
4
t=4
t
=
4
seconds? a)
∣
∫
0
4
v
(
t
)
d
t
∣
\displaystyle \left|\int_{0}^{4} v(t)\,dt\right|
∫
0
4
v
(
t
)
d
t
b)
∫
0
1
v
(
t
)
d
t
+
∫
3
4
v
(
t
)
d
t
\displaystyle \int_{0}^{1} v(t)\,dt+\int_{3}^{4} v(t)\,dt
∫
0
1
v
(
t
)
d
t
+
∫
3
4
v
(
t
)
d
t
c)
∫
0
4
∣
v
(
t
)
∣
d
t
\displaystyle \int_{0}^{4} |v(t)|\,dt
∫
0
4
∣
v
(
t
)
∣
d
t
d)
∫
0
4
v
(
t
)
d
t
\displaystyle \int_{0}^{4} v(t)\,dt
∫
0
4
v
(
t
)
d
t
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