Question

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y = x ; about x = 3

Answer 1

Answer:

Volume = π [ 2/3 - 12/2].

Step-by-step 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.