Use Greens Theorem to find the counterclockwise circulation and outward flux for the fields and curves. F
Question:
Use Green’s Theorem to find the counterclockwise circulation and outward flux for the fields and curves.
F = (y - 6x2)i + (x + y2)j
C: The triangle made by the lines y = 0, y = x, and x = 1
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THEOREM 5-Green's Theorem (Flux-Divergence or Normal Form) Let C be a piecewise smooth, simple closed curve enclosing a region R in the plane. Let F = Mi + Nj be a vector field with M and N having continuous first partial derivatives in an open region containing R. Then the outward flux of F across C equals the double integral of div F over the region R enclosed by C. fr-nds = M dy-1 Outward flux N dx = J R ƏM ON + dx dy ax dy Divergence integral (4)
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First lets parameterize the curve C For the line segment from 0 0 to 1 1 rt ti 0 ...View the full answer
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Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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