Arc length Find the length of the hypocycloid (or astroid)

Chapter 7, Problem 41E

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QUESTION:

Arc length  Find the length of the hypocycloid (or astroid) \(x^{2 / 3}+y^{2 / 3}=4\).

Questions & Answers

QUESTION:

Arc length  Find the length of the hypocycloid (or astroid) \(x^{2 / 3}+y^{2 / 3}=4\).

ANSWER:

Problem 41E

Arc length Find the length of the hypocycloid (or asteroid) .

Solution

Step 1

In this problem we have to find the length of the hypocycloid

The arc length is  … (1)

We have

Differentiating both sides with respect to , we get

     

… (2)

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