Question

Find the arc length of the curve on the interval [0, 2π].

Hypocycloid perimeter:  x = a cos3 θ, y = a sin3 θ

Answer 1

Step 1:

Hypo cycloid perimeter: , .

Arc length of the curve:

If a curve is described by parametric equations and ,

where are continuous on , then the arc length of the curve is

.

Consider .

Find  .

Find .

Step 2:

Substitute and values in the arc length formula.

Periodicity of is .

In the interval , we can write integral as four multiples of single integral considering in .

Step 3:

Solution:

Arc length of the curve is .