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4 Jan 2023
Let V = (x y) div V = curl V = Find F such that nabla F = V as follows: F(x, 0) - F(0, 0) = integral^x_0 v_i(t) middot c'(t) dt where c(t) = (t, 0) F(x, y) = F(0, 0)_(constant) + (first integral) (second integral) Check nabla F = Complete the following four integrals: integral^1_0 integral^2 pi_0 curl V r dr d theta which is integral^2 pi_0 v_i(t) middot c'(t) dt where c(t) = (cos (t), sin (t)) integral^1_0 integral^2 pi_0 div V r dr d theta which is integral^2 pi_0 V_c(t) middot r_c(t) dt
Let V = (x y) div V = curl V = Find F such that nabla F = V as follows: F(x, 0) - F(0, 0) = integral^x_0 v_i(t) middot c'(t) dt where c(t) = (t, 0) F(x, y) = F(0, 0)_(constant) + (first integral) (second integral) Check nabla F = Complete the following four integrals: integral^1_0 integral^2 pi_0 curl V r dr d theta which is integral^2 pi_0 v_i(t) middot c'(t) dt where c(t) = (cos (t), sin (t)) integral^1_0 integral^2 pi_0 div V r dr d theta which is integral^2 pi_0 V_c(t) middot r_c(t) dt
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