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Mathematics
Mathematics
Problem
Consider the parametric curve
x
(
t
)
=
t
2
x(t)=t^{2}
x
(
t
)
=
t
2
and
y
(
t
)
=
t
3
3
y(t)=\dfrac{t^{3}}{3}
y
(
t
)
=
3
t
3
for
0
≤
t
≤
T
0\le t\le T
0
≤
t
≤
T
. If the arc length of the curve on this interval equals
5
5
5
, determine the value of
T
T
T
(express your answer exactly).
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