(Solved): 6) Mass from linear density. Given a rod whose linear density function (x) (in mass per unit leng ...

6) Mass from linear density. Given a rod whose linear density function $?(x)$ (in mass per unit length) measures the density at the value $x$ over a region from $x=a$ to $x=b$, mass is defined by $\text{ mass }={?}_a^b?(x)dx.$ To visualize this with example sets of units: (1) $\underset{\mathrm{Kg}}{\underbrace{\mathrm{mass}}}={?}_a^b\underset{\mathrm{Kg}/\mathrm{m}}{\underbrace{?(x)}}\underset{\mathrm{m}}{\underbrace{dx}}$ : (2) $\underset{oz\text{. }}{\underbrace{\text{ mass }}}={?}_a^b\underset{ox./\mathrm{in}}{\underbrace{?(x)}}\underset{\text{in }}{\underbrace{dx}}$ Consider a thin rod oriented on the positive $x$-axis over the interval $[1,3]$ with linear density $?(x)=2x^2+3$. Determine the mass of the rod.