Answered: Let S be the part of the sphere x^2 +…

Let S be the part of the sphere x^2 + y^2 + z^2 = 1 that lies above the conez = sqrt(x^2 + y^2). Consider the integral∫ ∫sqrt(x^2 + y^2)dS.SHow to use spherical coordinate to evaluate it?

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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Question

Let S be the part of the sphere x^2 + y^2 + z^2 = 1 that lies above the cone
z = sqrt(x^2 + y^2). Consider the integral
∫ ∫sqrt(x^2 + y^2)dS.
S
How to use spherical coordinate to evaluate it?

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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