Answer:
Volume = π [ 2/3 - 12/2].
Explanation:
So, in this question we are asked to find or Calculate for or determine the value of volume v of the solid obtained by rotating the region bonded by the given curves about the specified lines = ? (Unknown). In addition, we are given that y = x, y = x , so, about x = 3.
Volume = π ∫ [ (3 - y)^2 - (3 - y)^2 ] dy.
(Taking 0 and 1 as the lower and upper limit).
Volume = π ∫ 9 - 6y + y^2 - 9 - 6y + y^2 dy.
(Taking 0 and 1 as the lower and upper limit).
Volume = π ∫ 2y^2 - 12y dy.
(Taking 0 and 1 as the lower and upper limit).
(Solving the quadratic equation above, we have; Roots: -6, 0
Root Pair: -3 ± 3
Factored: f(x) = 2(x + 6)x)
Also,
Volume = π [ 2y^3 / 3 - 12y2/2]
Volume = π [ 2/3 - 12/2] cubic units.