Let S denote the portion of the paraboloid z = 2² + y² with a ≤9. HINT: Both integrals should be nice if everything is set up correctly and you simplify! (a) Parameterize S. Note that in addition to finding an equation r(u, v) you also need to specify the domain restrictions on u and v. (b) Find the normal vector N for the parameterization you have found. (c) Use your work to evaluate the integral J₁ 22 x² + y² ds.

Let S denote the portion of the paraboloid z = 2² + y² with a ≤9. HINT: Both integrals should be nice if everything is set up correctly and you simplify! (a) Parameterize S. Note that in addition to finding an equation r(u, v) you also need to specify the domain restrictions on u and v. (b) Find the normal vector N for the parameterization you have found. (c) Use your work to evaluate the integral J₁ 22 x² + y² ds.

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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