Match the following integrals with the solid whose volume it represents. A. 2π∫30x5dx
B. 2π∫20y1+y2dy
C. 2π∫10(3−y)(1−y2)dy
D. 2π∫π/40(π−x)(cos(x)−sin(x))dx
1. The volume of the solid obtained by rotating the region described by 0≤y≤2,0≤x≤11+y2, about the x-axis, using cylindrical shells.
2. The volume of the solid obtained by rotating the region described by 0≤x≤3,0≤y≤x4, about the y-axis, using cylindrical shells.
3. The volume of the solid obtained by rotating the region bounded by x=y2, x=1, and y=0 about the line y=3, using cylindrical shells.
4. The volume of the solid obtained by rotating the region bounded by 0≤x≤π/4 and sin(x)≤y≤cos(x) about the line x=π, using cylindrical shells.