Solid Of Revolution Problem

Would you check this ,please?
Required the volume of solid formed by rotating area bounded by y=cosx,y=0,x=0,x=pi/2,about y=-1.
The answer given is 2pi+(pi^2)/4
Thank you.

Required volume
= π ∫ (x=0 to π/2) (1 + cosx)^2 dx
= π ∫ (x=0 to π/2) (1 + 2cosx + cos^2 x) dx
= π/2 ∫ (x=0 to π/2) (2 + 4cosx + 2cos^2 x) dx
= π/2 ∫ (x=0 to π/2) (2 + 4cosx + 1 + cos2x) dx
= π/2 [3x + 4sinx + (1/2)sin2x] ... (x=0 to π/2)
= π/2 [3π/2 + 4 - 0]
= (3/4) π^2 + 2π.

Answer differs.

yes
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