Consider the vector field F(x, y) = <3 + 2xy, x2 − 3y 2> (b) Evaluate...

Consider the vector field F(x, y) = <3 + 2xy, x2 − 3y 2> (b) Evaluate integral (subscript c) F · dr, where C is the curve (e^t sin t, e^t cost) for 0 ≤ t ≤ π.

Expert Solution

We evaluate the value of the given line integral by using conservative vector field and potential function.

milcah answered 2 years ago

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...

Solve the differential equation 1. a) 2xy"+ y' + y = 0 b) (x-1)y'' + 3y...

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1) Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 − 3)...

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A velocity vector field is given by F (x, y) = - i + xj a)...

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5. With each stated property, give an example of the 2-space vector field F(x,y). (a) F...

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Let f(x,y) be a scalar function, and let F(x,y,z) be a vector field. Only one of...

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If the hypothesis is (y)= f (+ X1, -X2,) what would be 2 or 3 x...

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Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along...

Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along the curve which is given by the intersection of the cylinder x 2 + y 2 = 4 and the plane x + y + z = 2 starting from the point (2, 0, 0) and ending at the point (0, 2, 0) with the counterclockwise orientation.

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