The given curve is rotated about the y-axis. Find the area of the resulting surface.

Question

y = 1/4x^2 − 1/2ln(x), 4 ≤ x ≤ 5

Answer 1

y' = x/2 - 1/(2x)
ds = √(1+y'^2) dx = √(1 + (x/2 - 1/(2x))^2) dx = 1/2 (x + 1/x) dx
so the surface area is
A = ∫2πr ds
where r = x
A = ∫[4,5] 2πx * 1/2 (x + 1/x) dx = 64π/3