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Let S be the surface obtained by rotating a smooth curve y = f(z), with a ≤ x ≤ b about the z-axis, where f(x) > 0. a) Find a parametrization r(u, v) of S. Hint: See figure below: (x, y, z) 24° b) Use this parametrization to show that the surface area of this surface of revolution is = f* ƒ(z) √/1 + (fº(z))}² dz. A = 2T

Let S be the surface obtained by rotating a smooth curve y = f(z), with a ≤ x ≤ b about the z-axis, where f(x) > 0. a) Find a parametrization r(u, v) of S. Hint: See figure below: (x, y, z) 24° b) Use this parametrization to show that the surface area of this surface of revolution is = f* ƒ(z) √/1 + (fº(z))}² dz. A = 2T

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let S be the surface obtained by rotating a smooth curve y = f(x), with a ≤ x ≤ b about the x-axis, where f(x) > 0. a) Find a parametrization r(u, v) of S. Hint: See figure below: (x, y, z) f(x) A = 2π 0 b) Use this parametrization to show that the surface area of this surface of revolution is = √² ƒ (2) √ 1 + (fº(z))² da. a
Transcribed Image Text:Let S be the surface obtained by rotating a smooth curve y = f(x), with a ≤ x ≤ b about the x-axis, where f(x) > 0. a) Find a parametrization r(u, v) of S. Hint: See figure below: (x, y, z) f(x) A = 2π 0 b) Use this parametrization to show that the surface area of this surface of revolution is = √² ƒ (2) √ 1 + (fº(z))² da. a
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