Step-by-step explanation:
The cross section per unit length is uniform, so ρ is constant.
The center of mass is therefore:
x_avg = (∫₀ᴸ x ρ dL) / (∫₀ᴸ ρ dL)
x_avg = (∫₀ᴸ x dL) / (∫₀ᴸ dL)
x_avg = (½ L²) / (L)
x_avg = ½ L
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