#### To determine

**To find:**

The total mass of the rod.

#### Answer

*1403 kg*

#### Explanation

**1) Concept:**

If the mass of the rod measured from the left end to a point *x* is *m(x)* then, the linear density is *ρx=m'(x)*.

Therefore, *mx=∫abρxdx* is the total mass of the rod lying between *x=a* and *x=b*.

**2) Given:**

*ρx=9+2x*

**3) Calculation:**

Consider

*ρx=9+2x*

Since *ρx=m'(x)*, the total mass of the rod lies between *x=0* and *x=4* is

*mx=∫04ρxdx*

*=∫049+2xdx*

Integrating using rules of integration we have,

*=9x+2x323204*

*=9x+4x32304*

*=94+44323-90+40323*

*=36+323-0*

*=108+323*

*=1403*

Therefore,

The total mass of the rod lyingbetween *x=0* and *x=4* is *1403 kg*

**Conclusion:**

Therefore,

The total mass of the rod is *1403 kg*