Let f(x, y) = 7x cos (y). Find the conservative vector field F, which is the gradient of f. (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) F = (7 cos(v).-7x sin(y)) Evaluate the line integral of F over the upper half of the unit circle centered at the origin, oriented clockwise. (Give an exact answer. Use symbolic notation and fractions where needed.) [F.dr Incorrect = 12

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let f(x, y) = 7x cos (y). Find the conservative vector field F, which is the gradient of f.
(Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and
fractions where needed.)
F = (7 cos (y).-7x sin(y)
Evaluate the line integral of F over the upper half of the unit circle centered at the origin, oriented clockwise.
(Give an exact answer. Use symbolic notation and fractions where needed.)
C
F. dr =
Incorrect
12
Question Source: Rogawski 4e Calculus Early Transcendentals
Publisher: W.H. Freema
5.02. D
Transcribed Image Text:Let f(x, y) = 7x cos (y). Find the conservative vector field F, which is the gradient of f. (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) F = (7 cos (y).-7x sin(y) Evaluate the line integral of F over the upper half of the unit circle centered at the origin, oriented clockwise. (Give an exact answer. Use symbolic notation and fractions where needed.) C F. dr = Incorrect 12 Question Source: Rogawski 4e Calculus Early Transcendentals Publisher: W.H. Freema 5.02. D
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