A rod with density $\delta(x) = x^2 + 2x$ lies on the x-axis between $x= 0$ and $x= 2$. Find the mass and center of mass of the rod.
I found mass by integrating $\int_0^2 \left(x^2+2x\right)$ and got 20/3.
I need help finding the center of mass.
2026-04-25 19:09:24.1777144164
A rod with density $\delta(x) = x^2+2x$ lies on the $x$-axis between $x= 0$ and $x= 2$. Find the mass and center of mass of the rod.
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The center of mass is in essence the average $x$
$$ \int_0^2 x \delta(x)\,{\rm d}x = x_{cm} \int_0^2 \delta(x)\,{\rm d}x $$
$$ x_{cm} = \dfrac{\int_0^2 x \delta(x)\,{\rm d}x}{\int_0^2 \delta(x)\,{\rm d}x} $$
$$ x_{cm} = \dfrac{ \frac{28}{3} } {\frac{20}{3} } = \frac{7}{5} = 1.4$$