Consider the graph of an ellipse C, oriented counterclockwise. Graphs of the vector fields F,, F,, F, and F, along the curve C are given (see figures). Along C, F, and F, are tangent to C, and F, and F, are normal to C. Determine whether the following integrals are positive, negative, or equal to 0. b. F, · T ds JF T ds а. ·T ds с. C d. F -T ds F -n ds f. F,•n ds е. g. F•n ds h. Fn ds Vectors of F1 along C Vectors of F2 along C Vectors of F3 along C Vectors of F4 along C

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the graph of an ellipse C, oriented counterclockwise.
Graphs of the vector fields F,, F,, F, and F, along the curve C are
given (see figures). Along C, F, and F, are tangent to C, and F,
and F, are normal to C. Determine whether the following integrals
are positive, negative, or equal to 0.
b. F, · T ds
JF T ds
а.
·T ds
с.
C
d.
F -T ds
F -n ds
f.
F,•n ds
е.
g.
F•n ds
h. Fn ds
Vectors of F1 along C
Vectors of F2 along C
Vectors of F3 along C
Vectors of F4 along C
Transcribed Image Text:Consider the graph of an ellipse C, oriented counterclockwise. Graphs of the vector fields F,, F,, F, and F, along the curve C are given (see figures). Along C, F, and F, are tangent to C, and F, and F, are normal to C. Determine whether the following integrals are positive, negative, or equal to 0. b. F, · T ds JF T ds а. ·T ds с. C d. F -T ds F -n ds f. F,•n ds е. g. F•n ds h. Fn ds Vectors of F1 along C Vectors of F2 along C Vectors of F3 along C Vectors of F4 along C
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