Let e, = (..÷) be a unit radial vector, where r = vx² + y² + z². (a) Calculate the integral of F = e"e, over the upper hemisphere of x + y + z? = 121 with the normal pointing outward. (Give your answer in exact form. Use symbolic notation and fractions where needed.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let e, = ( ) be a unit radial vector, where r = Vx² + y² + z?.
(a) Calculate the integral of F = e"e, over the upper hemisphere of x? + y² + z? = 121 with the normal
pointing outward.
(Give your answer in exact form. Use symbolic notation and fractions where needed.)
F. dS =
(b) Calculate the integral of F = 11e"e, over the octant x > 0, y 2 0, z > 0 of the unit sphere centered at the origin.
(Give your answer in exact form. Use symbolic notation and fractions where needed.)
F. dS =
Transcribed Image Text:Let e, = ( ) be a unit radial vector, where r = Vx² + y² + z?. (a) Calculate the integral of F = e"e, over the upper hemisphere of x? + y² + z? = 121 with the normal pointing outward. (Give your answer in exact form. Use symbolic notation and fractions where needed.) F. dS = (b) Calculate the integral of F = 11e"e, over the octant x > 0, y 2 0, z > 0 of the unit sphere centered at the origin. (Give your answer in exact form. Use symbolic notation and fractions where needed.) F. dS =
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