density and mass

Question

A rod with density δ(x)=8+sinx lies on the x-axis between x=0 and x=π. Find the x-value of the center of mass of the rod.

Enter the exact answer.

x¯⎯⎯=

Answer 1

Yefim has the correct answer, which is π/2. A nice way to see this result: The function is symmetric about π/2, so, as the interval is defined from 0 to π, π/2 is the center of mass.

Answer 2

x_c = ∫₀^πx(8 + sinx)dx/∫₀^π(8 + sinx)dx = 42.62/27.13 = 1.571