The mass of the rod is given by the linear density defined in kilograms as linear density*length.

The length of the rod is 4 m and the linear density is varying with `rho(x) = 5 + 2(x)^(1/2)`

The mass of the rod is the definite integral `int_(0)^4 rho(x) dx`

`int_(0)^45 + 2(x)^(1/2) dx`

=> `5x + 2*x^(3/2)/(3/2)` between 0 and 4

=> `5(4 - 0) + (4/3)(4^(3/2) - 0^(3/2))`

=> `20 + (4/3)*(8 - 0)`

=> `20 + 32/3`

=> `92/3`

The mass of the rod is `92/3` kg.