Question

Find the mass of the one-dimensional object. A wire that is 6 ft long (starting at x =0) and has a density function of rho(x) = x2+5x .

Answer 1

To find the mass of the one-dimensional wire, integrate the density function over the length of the wire.

Step-by-step explanation:

To find the mass of the one-dimensional wire, we need to integrate the density function over the length of the wire. The density function is given as rho(x) = x^2 + 5x. First, we need to find the limits of integration. The wire starts at x = 0 and is 6 ft long, so the limits are 0 and 6. The mass (m) is given by the integral of the density function over this interval:

m = ∫(0 to 6) (x^2 + 5x) dx = ∫(0 to 6) (x^2) dx + ∫(0 to 6) (5x) dx

Using the power rule for integration, we can evaluate these integrals to find the mass of the wire.