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Mathematics
Problem
Which of the following expressions gives the displacement of a particle from time
t
=
a
t=a
t
=
a
to time
t
=
b
t=b
t
=
b
if its velocity is
v
(
t
)
v(t)
v
(
t
)
? a)
(
b
−
a
)
v
(
a
+
b
2
)
(b-a)\,v\!\left(\dfrac{a+b}{2}\right)
(
b
−
a
)
v
(
2
a
+
b
)
b)
∫
a
b
v
(
t
)
d
t
\displaystyle \int_a^{b} v(t)\,dt
∫
a
b
v
(
t
)
d
t
c)
v
(
b
)
−
v
(
a
)
v(b)-v(a)
v
(
b
)
−
v
(
a
)
d)
∫
0
b
−
a
v
(
t
)
d
t
\displaystyle \int_{0}^{\,b-a} v(t)\,dt
∫
0
b
−
a
v
(
t
)
d
t
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