1.
The polar curve
r
=
g
(θ)
is parametrized by
x
=
g
(θ)
cos
θ,
y
=
g
(θ)
sin
θ.
Hence its arc length element is
ds
=
s
dx
d
θ
2
+
dy
d
θ
2
d
θ
=
q
(
g
0
(θ)
cos
θ

g
(θ)
sin
θ
)
2
+
(
g
0
(θ)
sin
θ
+
g
(θ)
cos
θ
)
2
d
θ
=
q
(
g
(θ)
)
2
+
(
g
0
(θ)
)
2
d
θ.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '12
 OnurFen
 Arc Length

Click to edit the document details