The linear density of a rod of length 4 m is given by rho (x) = 6 + 5 x measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the rod.

M (t) = 64 Kgs

Step-by-step explanation:

To find the total mass of the rod, we have to integrate the expression

M (x) = ∫₀⁴ rho (x) * dx

Where rho (x) = 6 + 5*x in Kgs / m

M (x) = ∫₀⁴ (6 + 5*x) dx ⇒ M (x) = ∫₀⁴ 6 dx + ∫₀⁴ 5*x dx

M (x) = 6x |₀⁴ + 5 * x²/2 |₀⁴

M (x) = 6 (4 - 0) + 5/2 (16 - 0)

M (x) = 24 + 40 Kgs

M (t) = 64 Kgs