Question

How do you do this question?

Answer 1

Step-by-step explanation:

S = ∫ 2π y ds

ds = √(1 + (dx/dy)²) dy

ds = √(1 + (8y)²) dy

ds = √(1 + 64y²) dy

S = ∫₁² 2π y √(1 + 64y²) dy

S = π/64 ∫₁² 128y √(1 + 64y²) dy

S = π/64 [⅔ (1 + 64y²)^(³/₂)] |₁²

S = π/96 (1 + 64y²)^(³/₂) |₁²

S = π/96 (1 + 256)^(³/₂) − π/96 (1 + 64)^(³/₂)

S = π/96 (257√257) − π/96 (65√65)

S = π/96 (257√257 − 65√65)