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Mathematics
Mathematics
Problem
A curve is defined piecewise by Piece A
(
1
≤
t
≤
e
)
:
x
=
t
,
y
=
ln
t
(1 \le t \le e): \; x = t, \; y = \ln t
(
1
≤
t
≤
e
)
:
x
=
t
,
y
=
ln
t
Piece B
(
e
≤
t
≤
e
+
3
)
:
x
=
e
,
y
=
1
+
(
t
−
e
)
2
(e \le t \le e+3): \; x = e, \; y = 1 + (t-e)^{2}
(
e
≤
t
≤
e
+
3
)
:
x
=
e
,
y
=
1
+
(
t
−
e
)
2
Compute the total length of the curve from
t
=
1
t = 1
t
=
1
to
t
=
e
+
3
t = e + 3
t
=
e
+
3
.
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