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## Homework Statement

A wire is shaped like the astroid x=cos

^{3}(t), y=sin

^{3}(t), t[0, 2*pi] and has constant density = k. Find its moment of intertia I

_{0}around the origin.

**2. The attempt at a solution**

To find the MOE we must integrate

**k* (x**along the curve. We differentiate and find that

^{2}+ y^{2})ds*ds*can be written

*3*cos(t)*sin(t)*.The final expression is:

**3k * Int (cos**for t [0, 2*pi]. But this is zero! What/where is my mistake?

^{7}(t)*sin(t) + sin^{7}(t)*cos(t))dt