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Riley hobson bence
· Problem 2.48
Preliminary calculus
Mathematics — Methods · arc-length-parametric
Problem
Show that the total length of the astroid
x
2
/
3
+
y
2
/
3
=
a
2
/
3
x^{2/3} + y^{2/3} = a^{2/3}
x
2/3
+
y
2/3
=
a
2/3
, which can be parameterised as
x
=
a
cos
3
θ
x = a\cos^3\theta
x
=
a
cos
3
θ
,
y
=
a
sin
3
θ
y = a\sin^3\theta
y
=
a
sin
3
θ
, is
6
a
6a
6
a
.
Related theory
Regular Curves And Arc Length
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