Answer:
22.51 unit^3 to nearest hundredth.
Explanation:
First find the points of intersection of the 2 functions:
y = (x - 2)^2
y = x
So x = (x - 2)^2
x^2 - 4x + 4 - x = 0
x^2 - 5x + 4 = 0
(x - 1)( x - 4) = 0
So they intersect at (1, 1) and (4,4).
y = (x - 2)^2
----> x - 2 = √y
----> x = √y + 2
Required volume
4
= ∫π (√y + 2)^2 dy - ∫π y^2 dy
1
4
= π ∫( y + 2√y + 4) dy - π ∫ y^2 dy
1
4
= π [ y^2/2 + 2y^3/2 / 3/2 + 4y] - [π[y^3/3]
1
= π [8 + 10.666 + 16] - [0.5 + 2 + 4} - π[21.333- 0.333]
= 88.486 - 65.973
= 22.513.