Let F= (y-r, z²+y) and C be the closed, piece-wise smooth curve in the zy-plane consisting of: C: the directed line segment from (a,0) → (a, a), followed by C: the directed line segment from (a, a) → (0, a), followed by; C3: the path along the quarter circle + y² = a? from (0, a) -→ (a,0). a) For what values of a >0 is fF. dr = 0? b) Is the line integral f.F- dr path-independent on R?? Explain.
Let F= (y-r, z²+y) and C be the closed, piece-wise smooth curve in the zy-plane consisting of: C: the directed line segment from (a,0) → (a, a), followed by C: the directed line segment from (a, a) → (0, a), followed by; C3: the path along the quarter circle + y² = a? from (0, a) -→ (a,0). a) For what values of a >0 is fF. dr = 0? b) Is the line integral f.F- dr path-independent on R?? Explain.
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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