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