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A square sheet of aluminum is uniformly 1.5mm thickIt was cut to the shape shown along the function y xb (b 0.45)?

A square sheet of aluminum is uniformly 1.5mm thickIt was cut to the shape shown along the function y xb (b 0.45), and retaining the part below the curveThe density of aluminum is ρ 2.70x103 kg/m3.1) Calculate Iy, the moment-of-inertia about the y-axis, of the piece of aluminum sheet shown in the figure above.2) Calculate Ix, the moment-of-inertia about the x-axis, of the piece of aluminum sheet shown in the figure above.I can't seem to figure this out.

Answer:

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Iint of r^2 dm dm is mass, we dont have mass but we do have density,p and thickness, t, hence: dmpdV dV is volume, we dont have it, so: dV tdA Ipt int of r^2 dA a) we rotate about x-axis, so dAy dx x^b dx, and rx Iy int from 0 to 1 pt[x^b x^2]dxpt/3+b(solve for Iy b) rotate about y-axis, so dA(1-x)dy(1-y^1/b)dy, and ry Ix int from 0 to 1 pt[(1-y^1/b)y^2]dypt[1/3-1/(3+1/b)] (solve for Ix) good luck
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