Repeat a logarithmic segment with the correct jump values

Let $f(x)=\ln x$ for $1\le x\le e$, and $f(x)=0$ for $e<x\le3$, with $f(x+2)=f(x)$ for all real $x$.

(a) Rotate the region bounded by $y=f(x)$, the x-axis and $x=e$ through $2\pi$ about the x-axis. Find the exact volume.

(b) Sketch $y=f(x)$ for $-3\le x\le4$. Hence find $\int_{-3}^4f(x)dx$.