(a) Find a vector parametric equation for the ellipse that lies on the plane x +2y+z=3 and inside the cylinder x² + y² = 16. F(u, v) = ¯ for 0 ≤ u ≤ 4 and 0 ≤ v ≤ 2m. (b) dA = F₁ × Tv = (c) dA= = ||ďA|| = ||Tu × Tv|| -0 Surface area = = (d) Set up and evaluate a double integral for the surface area of the ellipse.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a) Find a vector parametric equation for the ellipse that lies on the plane x +2y+z=3 and inside the cylinder x² + y² = 16.
ŕ(u, v) = for 0 ≤ u ≤ 4 and 0 ≤ v ≤ 2m.
(b) d1 =ở xổ
(c) dA = ||ďA|| = || Fu × Ťv || =0
(d) Set up and evaluate a double integral for the surface area of the ellipse.
Surface area =
=
Transcribed Image Text:(a) Find a vector parametric equation for the ellipse that lies on the plane x +2y+z=3 and inside the cylinder x² + y² = 16. ŕ(u, v) = for 0 ≤ u ≤ 4 and 0 ≤ v ≤ 2m. (b) d1 =ở xổ (c) dA = ||ďA|| = || Fu × Ťv || =0 (d) Set up and evaluate a double integral for the surface area of the ellipse. Surface area = =
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