1) Volume created when the area bounded by the x-axis, the y-axis, and the line y = -3x+5 is rotated about:

Question

a) the y-axis
b) the line y = 6

2) Volume created when the area bounded by x = 3y-y^2 and the y-axis is rotated about the x-axis

Answer 1

#1
(a) discs ∫[0,5] π((5-y)/3)^2 dy
(a) shells ∫[0,5/3] 2πx(5-3x) dx
(b) shells ∫[0,5] 2π(6-y)(5-y)/3 dy

#2
discs ∫[0,9/4] π(((3+√(9-4x))/2)^2-(((3-√(9-4x)))/2)^2) dx
shells ∫[0,3] 2πy(3y-y^2) dy

Answer 2

#1
(a) 14.544 units^3
(b) 113.446 units^3

#2: 6.75 units^3

is this correct?

Answer 3

I find it easier to leave the π in the answer. That way it's exact, instead of some decimal approximation. In any case, I got

(a) 20π/9
(b) 125π/27

#2 27π/2