The linear density of a rod of length 4 m is given by 𝜌(x) = 8 + 7 radical 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.

Question

The linear density of a rod of length 4 m is given by 𝜌(x) = 8 + 7 radical 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.

𝜌(x) = 8 + 7x

Answer 1

m = ∫₀⁴(8 + 7√x)dx = (8x + 14/3x^3/2)₀⁴ = 32 + 14/3·8 = 32 + 112/3 = 208/3 = 69.333 kg