Question

Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C. F(x, y) = (6x^2 + y)i + 4xy^2j C: boundary of the region lying between the graphs of y = ?x, y = 0, and x = 16 Step 1 To find the work done by the force F on the particle, apply Green's Theorem. Recall that according to Green's Theorem, if M and N have continuous first partial derivatives in an open region containing R, then ?_C M dx + N dy = ?_R (?N/?x - ?M/?y) dA. Let W be the work done of the force F on a particle that is moving counterclockwise around the closed path C. Work = ?_C (6x^2 + y) dx + 4xy^2 dy = ?_R (?N/?x - ?M/?y) dA. Because M = 6x^2 + y and N = [] xy^2, it follows that ?N/?x = [] and ?M/?y = [].

          Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C.
F(x, y) = (6x^2 + y)i + 4xy^2j
C: boundary of the region lying between the graphs of y = ?x, y = 0, and x = 16
Step 1
To find the work done by the force F on the particle, apply Green's Theorem.
Recall that according to Green's Theorem, if M and N have continuous first partial derivatives in an open region containing R, then
?_C M dx + N dy = ?_R (?N/?x - ?M/?y) dA.
Let W be the work done of the force F on a particle that is moving counterclockwise around the closed path C.
Work = ?_C (6x^2 + y) dx + 4xy^2 dy = ?_R (?N/?x - ?M/?y) dA.
Because M = 6x^2 + y and N = [] xy^2, it follows that
?N/?x = [] and ?M/?y = [].

Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C.
F(x, y) = (6x^2 + y)i + 4xy^2j
C: boundary of the region lying between the graphs of y = ?x, y = 0, and x = 16
Step 1
To find the work done by the force F on the particle, apply Green's Theorem.
Recall that according to Green's Theorem, if M and N have continuous first partial derivatives in an open region containing R, then
?C M dx + N dy = ?R (?N/?x - ?M/?y) dA.
Let W be the work done of the force F on a particle that is moving counterclockwise around the closed path C.
Work = ?C (6x^2 + y) dx + 4xy^2 dy = ?R (?N/?x - ?M/?y) dA.
Because M = 6x^2 + y and N = [] xy^2, it follows that
?N/?x = [] and ?M/?y = [].

Added by Casey D.

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