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

A. $\displaystyle \pi \int_{0}^{\,\pi/2} {\cos^2(x)}\, dx$
B. $\displaystyle \pi \int_{2}^{\,5} {y}\, dy$
C. $\displaystyle \pi \int_{0}^{\,1} {(y^4-y^8)}\, dy$
D. $\displaystyle \pi \int_{0}^{\,\pi/2} {[(1+\cos(x))^2-1^2]}\, dx$

1. The volume of the solid obtained by rotating the region described by $\,0 \le x \le \pi/2,\,0 \le y \le \cos(x),$ about the $x$-axis.
2. The volume of the solid obtained by rotating the region described by $0 \le y \le 1,\,y^4 \le x \le y^2,$ about the $y$-axis.
3. The volume of the solid obtained by rotating the region described by $2 \le y \le 5,\,0 \le x \le \sqrt{y},$ about the $y$-axis.
4. The volume of the solid obtained by rotating the region described by $0 \le x \le \pi/2,\,0 \le y \le \cos(x),$ about the line $y=-1$.