Let e,= (,) be a unit radial vector, where r = √√x² + y² + z². er (a) Calculate the integral of F = eer over the upper hemisphere of x² + y² + z² = 121 with the normal pointing outward. (Give your answer in exact form. Use symbolic notation and fractions where needed.) [[F FdS: (b) Calculate the integral of F = 11eer over the octant x ≥ 0, y ≥ 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.0 F.dS=

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Let e,= (,) be a unit radial vector, where r = √√x² + y² + z².
er
(a) Calculate the integral of F = eer over the upper hemisphere of x² + y² + z² = 121 with the normal pointing outward.
(Give your answer in exact form. Use symbolic notation and fractions where needed.)
[[F
FdS:
(b) Calculate the integral of F = 11eer over the octant x ≥ 0, y ≥ 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.0
F.dS=
Transcribed Image Text:Let e,= (,) be a unit radial vector, where r = √√x² + y² + z². er (a) Calculate the integral of F = eer over the upper hemisphere of x² + y² + z² = 121 with the normal pointing outward. (Give your answer in exact form. Use symbolic notation and fractions where needed.) [[F FdS: (b) Calculate the integral of F = 11eer over the octant x ≥ 0, y ≥ 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.0 F.dS=
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