Question

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.

Answer 1

M(t) = 64 Kgs

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