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## Homework Statement

The first quadrant area bounded by the curve

[tex]x^3+y^3=8[/tex]

is rotated around y-axis to give a solid of rotation. The question asks for an integral which represents the solid's moment of inertia around the axis.

My answer is:

[tex]I_y=M\frac{\int_0^2x^2ydx}{\int_0^2x^2dx}[/tex]

but seems like I'm wrong. Could someone help me out, please?