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Mathematics
Mathematics
Problem
The curve is defined by
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
≤
1
0\le t\le 1
0
≤
t
≤
1
. Which of the following is the exact length of the curve on this interval? a)
1
2
(
5
5
−
8
)
\dfrac{1}{2}\bigl(5\sqrt{5}-8\bigr)
2
1
(
5
5
−
8
)
b)
1
3
(
5
5
)
\dfrac{1}{3}\bigl(5\sqrt{5}\bigr)
3
1
(
5
5
)
c)
1
3
(
5
5
−
8
)
\dfrac{1}{3}\bigl(5\sqrt{5}-8\bigr)
3
1
(
5
5
−
8
)
d)
1
3
(
5
5
+
8
)
\dfrac{1}{3}\bigl(5\sqrt{5}+8\bigr)
3
1
(
5
5
+
8
)
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