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Mathematics
Mathematics
Problem
A path consists of two consecutive parametric segments: Segment I:
x
(
t
)
=
t
,
y
(
t
)
=
0
,
0
≤
t
≤
3
x(t)=t,\;y(t)=0,\;0\le t\le 3
x
(
t
)
=
t
,
y
(
t
)
=
0
,
0
≤
t
≤
3
. Segment II:
x
(
θ
)
=
3
+
2
cos
θ
,
y
(
θ
)
=
2
sin
θ
,
0
≤
θ
≤
π
2
x(\theta)=3+2\cos\theta,\;y(\theta)=2\sin\theta,\;0\le \theta\le\dfrac{\pi}{2}
x
(
θ
)
=
3
+
2
cos
θ
,
y
(
θ
)
=
2
sin
θ
,
0
≤
θ
≤
2
π
. Determine the total length of the complete path. a)
3
+
π
2
3+\dfrac{\pi}{2}
3
+
2
π
b)
2
π
2\pi
2
π
c)
3
+
π
3+\pi
3
+
π
d)
3
+
2
π
3+2\pi
3
+
2
π
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