Question

Given a thin rod along the x-axis over the interval [a,b], let rho(x) denote a linear density function giving the density of the rod at a point x in the interval. Then the mass of the rod is given by:___________.

Answer 1

Answer:

$m = \int\limits^a_b \rho(x) \, dx$

Step-by-step explanation:

The linear density is given by$\dfrac{dm}{dx}$.

$\rho(x) = \dfrac{dm}{dx}$

$dm = \rho(x)\,dx$

Integraring both sides to get the mass,

$m = \int\!\rho(x) \, dx + C$

C is the constant of integration.

With x between a and b,

$m = \int\limits^a_b \rho(x) \, dx$