Surface area of an ellipsoid Consider the ellipsoid x 2 /a 2 + y 2 /b 2 + z 2 /c 2 = 1, where a , b , and c are positive real numbers. a. Show that the surface is described by the parametric equations r ( u , v ) = 〈 a cos u sin v , b sin u sin v , c cos v 〉 for 0 ≤ u ≤ 2 π , 0 ≤ v ≤ π . b. Write an integral for the surface area of the ellipsoid.
Surface area of an ellipsoid Consider the ellipsoid x 2 /a 2 + y 2 /b 2 + z 2 /c 2 = 1, where a , b , and c are positive real numbers. a. Show that the surface is described by the parametric equations r ( u , v ) = 〈 a cos u sin v , b sin u sin v , c cos v 〉 for 0 ≤ u ≤ 2 π , 0 ≤ v ≤ π . b. Write an integral for the surface area of the ellipsoid.
Solution Summary: The author explains how the given surface is described by the parametric equations r(u,v)=langle amathrmcos
Surface area of an ellipsoid Consider the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1, where a, b, and c are positive real numbers.
a. Show that the surface is described by the parametric equations
r(u, v) = 〈a cos u sin v, b sin u sin v, c cos v〉
for 0 ≤ u ≤ 2π, 0 ≤ v ≤ π.
b. Write an integral for the surface area of the ellipsoid.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Surface area of an ellipsoid Consider the ellipsoidx2/a2 + y2/b2 + z2/c2 = 1, where a, b, and c are positive real numbers.a. Show that the surface is described by the parametric equations r(u, ν) = ⟨a cos u sin ν, b sin u sin ν, c cos ν⟩ for 0 ≤ u ≤ 2π, 0 ≤ ν ≤ π.b. Write an integral for the surface area of the ellipsoid.
Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.
Sketch the graph of the parametric surface. x= sinh u, y=v, z=2cosh u.
Chapter 17 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
Thomas' Calculus: Early Transcendentals (14th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.