A wire is shaped like the astroid x=cos3(t), y=sin3(t), t[0, 2*pi] and has constant density = k. Find its moment of intertia I0 around the origin.
2. The attempt at a solution
To find the MOE we must integrate k* (x2 + y2)ds along the curve. We differentiate and find that ds can be written 3*cos(t)*sin(t).The final expression is:
3k * Int (cos7(t)*sin(t) + sin7(t)*cos(t))dt for t [0, 2*pi]. But this is zero! What/where is my mistake?