Match the following integrals with the solid whose volume it represents.

A. $\displaystyle 2\pi \int_{0}^{\,3} {x^5}\, dx$
B. $\displaystyle 2\pi \int_{0}^{\,2} {\frac{y}{1+y^2}}\, dy$
C. $\displaystyle 2\pi \int_{0}^{\,1} {(3-y)(1-y^2)}\, dy$
D. $\displaystyle 2\pi \int_{0}^{\,\pi/4} {(\pi-x)(\cos(x)-\sin(x))}\, dx$

1. The volume of the solid obtained by rotating the region described by $0 \le x \le 3,\,0 \le y \le x^4,$ about the $y$-axis, using cylindrical shells.
2. The volume of the solid obtained by rotating the region bounded by $x=y^2,$ $x=1,$ and $y=0$ about the line $y = 3$, using cylindrical shells.
3. The volume of the solid obtained by rotating the region described by $0 \le y \le 2,\,0 \le x \le \frac{1}{1+y^2},$ about the $x$-axis, using cylindrical shells.
4. The volume of the solid obtained by rotating the region bounded by $0 \le x \le \pi/4$ and $\sin(x) \le y \le \cos(x)$ about the line $x=\pi,$ using cylindrical shells.