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Original Question
The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 3 − x2, 0 ¡Ü x ¡Ü 4Question
The given curve is rotated about the y-axis. Find the area of the resulting surface.
y = 1/4x^2 − 1/2ln(x), 4 ≤ x ≤ 5
y = 1/4x^2 − 1/2ln(x), 4 ≤ x ≤ 5
Answers
oobleck
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
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