(Solved): (4) (7 pts) Set up, but do NOT evaluate, the integral needed to determine the mass M of a tree trun ...

(4) (7 pts) Set up, but do NOT evaluate, the integral needed to determine the mass $M$ of a tree trunk cross section with a radius of $2\mathrm{m}$ and radial density approximated by $?(x)=\sqrt{2+\cos (?x)}$, in $\mathrm{kg}/{\mathrm{m}}^2$, with $x$ in meters $(\mathrm{m})$. Do NOT Evaluate. $M=$ Units: (5) (10 pts) A spring that obeys Hooke's law has a spring constant $k=4\mathrm{N}/\mathrm{m}$ and a natural length $l=6$ meters $(m)$. This spring starts in an initial position held stretched 2 meters longer than its natural length. Compute the additional work (and units) required to stretch the spring from the initial position given to being fully stretched 4 meters longer than its natural length.