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Mathematics
Mathematics
Problem
A path in the plane is traced in two parts. Segment 1
(
0
≤
t
≤
2
)
:
x
=
t
,
y
=
t
2
2
(0 \le t \le 2): \; x=t, \; y=\dfrac{t^{2}}{2}
(
0
≤
t
≤
2
)
:
x
=
t
,
y
=
2
t
2
Segment 2
(
2
≤
t
≤
4
)
:
x
=
2
,
y
=
t
(2 \le t \le 4): \; x = 2, \; y = t
(
2
≤
t
≤
4
)
:
x
=
2
,
y
=
t
Determine the exact total length of the path from
t
=
0
t = 0
t
=
0
to
t
=
4
t = 4
t
=
4
.
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