Use Greens Theorem to find the counterclockwise circulation and outward flux for the field F and curve
Question:
Use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F and curve C.F = (x2 + 4y)i + (x + y2)j
C: The square bounded by x = 0, x = 1, y = 0, y = 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-May- Outward flux - N dx = JI ( T ax R = aM ƏN dy Divergence integral dx dy (4)
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To find the counterclockwise circulation and outward flux for the vector field F x2 4yi x y2j around the square bounded by x 0 x 1 y 0 y 1 we can apply Greens theorem Greens theorem states that the co...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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