(a) Find a vector parametric equation for the ellipse that lies on the plane x + 3y + z = 5 and inside the cylinder x² + y² = 49. ř (u, v) = ■ for 0 ≤ u ≤ 7 and 0 ≤ v ≤ 2π. (b) dA = ₁ × v น (c) dA= ||WA|| = || u xơ (d) Set up and evaluate a double integral for the surface area of the ellipse. Surface area = =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Find a vector parametric equation for the ellipse that lies on the plane x + 3y + z = 5 and inside the cylinder x² + y² = 49.
ř (u, v) =
=
for 0 ≤ u ≤ 7 and 0 ≤ v ≤ 2π.
(b) dA = ₂ × v
=
(c) dA = ||dA|| = ||Ťu × 7v||
Surface area =
=
(d) Set up and evaluate a double integral for the surface area of the ellipse.
Transcribed Image Text:(a) Find a vector parametric equation for the ellipse that lies on the plane x + 3y + z = 5 and inside the cylinder x² + y² = 49. ř (u, v) = = for 0 ≤ u ≤ 7 and 0 ≤ v ≤ 2π. (b) dA = ₂ × v = (c) dA = ||dA|| = ||Ťu × 7v|| Surface area = = (d) Set up and evaluate a double integral for the surface area of the ellipse.
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