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Let R and a be real numbers such that 0 < a < R. Let S be the surface parametrized by r(u, v) = (R+ a cos(u)) cos(v)i + (R+a cos(u)) sin(v)j+a sin(u)k, where 0 < u < 2n and 0 < v < 2n. (a) Describe and draw S. (b) Find the surface area of S. ? + y²) do. (x2. (c) Evaluate

Let R and a be real numbers such that 0 < a < R. Let S be the surface parametrized by r(u, v) = (R+ a cos(u)) cos(v)i + (R+a cos(u)) sin(v)j+a sin(u)k, where 0 < u < 2n and 0 < v < 2n. (a) Describe and draw S. (b) Find the surface area of S. ? + y²) do. (x2. (c) Evaluate

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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The problem I'm solving is within the screenshot. I had a problem with part c. When I substituted the integrand for the parametrization, I didn't know how to integrate the expression (R+acosu)^3. Thank you very much!

Let R and a be real numbers such that 0 < a < R. Let S be the surface parametrized by r(u, v) = (R+ acos(u)) cos(v)i + (R+a cos(u)) sin(v)j+a sin(u)k, where 0 < u < 2n and 0 < v < 2n. (a) Describe and draw S. (b) Find the surface area of S. (c) Evaluate (x² + y³ ) do. S
Transcribed Image Text:Let R and a be real numbers such that 0 < a < R. Let S be the surface parametrized by r(u, v) = (R+ acos(u)) cos(v)i + (R+a cos(u)) sin(v)j+a sin(u)k, where 0 < u < 2n and 0 < v < 2n. (a) Describe and draw S. (b) Find the surface area of S. (c) Evaluate (x² + y³ ) do. S
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