Question Four(a) Verify Green's theorem in the plane for fe(3a2-8y2) da +(4y - 6xy) dy, whereC is the boundary of the region y = √ andY=(b) If F(x, y, z)= azi+3ayj-22k, evaluate J, F-dS using Gauss's theorem when Sis the closed cylinder bounded by the surface a² + y2 = 1 and the planes z = 0and z = 3.(c) Show that if is continuously differentiable in a given region V and on itsboundary S, thenfødsdS= √₁ 760Vødv

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Verify Green's theorem in the plane for fe(3a²-8y2) da +(4y - 6ay) dy, where C is the boundary of the region y √ and

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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