Calculus!!!?

Question

Use the region bounded by y=10-x^2, x=1, x=3, y=0 and use the discs to find the volume below.
a-Revolve the region around the x- axis
b-Revolve the region around the line y=-1

Answer 1

b

Answer 2

a) V = π∫(1 to 3) (10-x^2)^2 dx
= π∫(1 to 3) (100 - 20x^2 + x^4) dx
= π [100x - 20/3 x^3 + 1/5 x^5][1 to 3]
= π (300 - 180 + 243/5 - 100 + 20/3 - 1/5)
= 1126π/15.

b) V = π∫(1 to 3) [(y+1)^2 - 1^2] dx
= π∫(1 to 3) (120 - 22x^2 + x^4) dx
= π [120x - 22/3 x^3 + 1/5 x^5][1 to 3]
= π (360 - 198 + 243/5 - 120 + 22/3 - 1/5)
= 1466π/15.

Answer 3

a