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If a € IR', which of the following expressions or triple integrals is NOT equal to the volume of a sphere with equation x² + y² + z² = a²? O 2 Ꮭ Ꮭ Ꭻ a2 _2 7Ꭲ . 4 Jờ Jo Jo p sin ¢ dp dò dê 27 2 2 fᎢ Ꭻ Ꭻ O 4fa So q² rdz dr de a? _x? Ꮭ rdz dr de a- x2 _y? dz dy dx

If a € IR', which of the following expressions or triple integrals is NOT equal to the volume of a sphere with equation x² + y² + z² = a²? O 2 Ꮭ Ꮭ Ꭻ a2 _2 7Ꭲ . 4 Jờ Jo Jo p sin ¢ dp dò dê 27 2 2 fᎢ Ꭻ Ꭻ O 4fa So q² rdz dr de a? _x? Ꮭ rdz dr de a- x2 _y? dz dy dx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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If a € R+, which of the following expressions or triple integrals is NOT equal to the volume of a sphere with equation x² + y² + z² = a²? 2 fő fő So a²-p² 2π 2 f²™ So So π 4 f² fő fő p² sin dp dó de r dz dr do a²_r² a²-x² 2 r dz dr do So a²-x²-y² 4 Sªa So None of the given choices dz dy dx
Transcribed Image Text:If a € R+, which of the following expressions or triple integrals is NOT equal to the volume of a sphere with equation x² + y² + z² = a²? 2 fő fő So a²-p² 2π 2 f²™ So So π 4 f² fő fő p² sin dp dó de r dz dr do a²_r² a²-x² 2 r dz dr do So a²-x²-y² 4 Sªa So None of the given choices dz dy dx
What is the meaning of path independence of a vector field F? The vector field assumes the same values on any two paths between two fixed points. F(Q) – F(P) has the same value for all points P and Q in the domain of the vector field. None of the given choices All line integrals of F (over any path) have the same value. O All line integrals of F between two fixed points have the same value.
Transcribed Image Text:What is the meaning of path independence of a vector field F? The vector field assumes the same values on any two paths between two fixed points. F(Q) – F(P) has the same value for all points P and Q in the domain of the vector field. None of the given choices All line integrals of F (over any path) have the same value. O All line integrals of F between two fixed points have the same value.
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