3. a) Consider the vector field F(x, y, z) = (2xy2 z, 2x 2 yz, x2...

3. a) Consider the vector field F(x, y, z) = (2xy2 z, 2x 2 yz, x2 y 2 ) and the curve r(t) = (sin t,sin t cost, cost) on the interval [ π 4 , 3π 4 ]. Calculate R C F · dr using the definition of the line integral. [5] b) Find a function f : R 3 → R so that F = ∇f. [5] c) Verify your answer from (a) using (b) and the Fundamental Theorem for Line Integrals. [5]

Expert Solution

milcah answered 2 years ago

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