Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit 0 ≤ y ≤ 2; x ≥ 0; z ≥ 0. (a) Suppose that S is parameterized by r(θ, y) = (3 cos(θ), y, 3 sin(θ)) whit θ in [0,π/2]; and y in [0, 2] , Use this parametrization to find the area of ´ S. (b) Justify that ~ n = (x = 3,0; z = 3) is a vector normal to S, and use it to find the value of the surface integral ∫ ∫ FndS, where F(x; y; z) = (3x,y^5,3z).

Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit 0 ≤ y ≤ 2; x ≥ 0; z ≥ 0. (a) Suppose that S is parameterized by r(θ, y) = (3 cos(θ), y, 3 sin(θ)) whit θ in [0,π/2]; and y in [0, 2] , Use this parametrization to find the area of ´ S. (b) Justify that ~ n = (x = 3,0; z = 3) is a vector normal to S, and use it to find the value of the surface integral ∫ ∫ FndS, where F(x; y; z) = (3x,y^5,3z).

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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