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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Can you answer question 3 please
Transcribed Image Text:3. Let S denote the portion of the paraboloid z = 2² + y² with z 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 d
2z
x² + y²
JIS T²
(d) Use your work to evaluate
tation.
work to evaluate (yi- aj + z(x² + y²)k). d5 assuming downward orien-
S
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