Ava45018 Ava45018
  • 01-10-2020
  • Mathematics
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How do you do this question?

How do you do this question class=

Respuesta :

MathPhys
MathPhys MathPhys
  • 01-10-2020

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)

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