Consider the vector field F = (y, –x, x² + y²). Find the flux of F through S if: (a) S the part of the upside-down paraboloid z = 9 – x² – y² above the xy-plane, oriented upward. (b) S is the boundary of the bounded region between the xy-plane and the graph of z = 9 – x2 – y².
Consider the vector field F = (y, –x, x² + y²). Find the flux of F through S if: (a) S the part of the upside-down paraboloid z = 9 – x² – y² above the xy-plane, oriented upward. (b) S is the boundary of the bounded region between the xy-plane and the graph of z = 9 – x2 – y².
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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Transcribed Image Text:3. Consider the vector field F = (y,=x,x² + y²). Find the flux of F through S if:
(a) S the part of the upside-down paraboloid z = 9 – x² – y² above the xy-plane,
oriented upward.
(b) S is the boundary of the bounded region between the xy-plane and the graph
of z = 9 – x2 – y².
4. Let F = (-2, y). Compute the line integral of F over each curve.
(a) C1 is the top half of the unit circle, oriented counterclockwise.
(h) C2 is the entire unit circle, oriented counterclockwise.
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