Given curve is a boundary of domain {[r. y] ER + y 4 Ar0 Ay0}...

 

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Given curve is a boundary of domain {[r. y] ER² ² + y² ≤4 Ar≥0 Ay≥0} oriented counter-clockwise. (a) Compute circulation of f(x,y) = (-ry, y²+2y) over the curve. (b) Suggest another approach of the computation (just one equality). For a vector function f(x, y) = (-In(x² + y²), 1) compute the circulation over a curve: (a) {[y] R² + y² = 1} oriented counter-clockwise. (b) {[] R2: (-1)²+ y² = 1} oriented counter-clockwise. (c) C is boundary of a square with a center [3.1] and side length a=2 oriented positively. Given a curve C-C₁UC, where C₁ is a line between points [1: √2] and [1: -√2] and C2={.y] R2: (2-1)² + y² = 2 Az≤ 1} oriented clockwise. Compute (r. 1). ds. Given curve is a boundary of a triangle P = [1:1], Q = [21], R = [2:3] oriented respectively. Compute .ds. : .Given curve is a boundary of domain {[ry] € R² y ≥2 Ar≥ 0 A y ≤ 1} oriented negatively. Compute the circulation of a vector field f(x, y) = (-y/2.x/2) over the curve. Given curve is a boundary of domain {[r. y] ER² ² + y² ≤4 Ar≥0 Ay≥0} oriented counter-clockwise. (a) Compute circulation of f(x,y) = (-ry, y²+2y) over the curve. (b) Suggest another approach of the computation (just one equality). For a vector function f(x, y) = (-In(x² + y²), 1) compute the circulation over a curve: (a) {[y] R² + y² = 1} oriented counter-clockwise. (b) {[] R2: (-1)²+ y² = 1} oriented counter-clockwise. (c) C is boundary of a square with a center [3.1] and side length a=2 oriented positively. Given a curve C-C₁UC, where C₁ is a line between points [1: √2] and [1: -√2] and C2={.y] R2: (2-1)² + y² = 2 Az≤ 1} oriented clockwise. Compute (r. 1). ds. Given curve is a boundary of a triangle P = [1:1], Q = [21], R = [2:3] oriented respectively. Compute .ds. : .Given curve is a boundary of domain {[ry] € R² y ≥2 Ar≥ 0 A y ≤ 1} oriented negatively. Compute the circulation of a vector field f(x, y) = (-y/2.x/2) over the curve.

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a To compute the circulation of the vector field fx y ry y2 29 over the curve we can parametrize the curve and evaluate the line integral The curve is defined by the inequality A y 0 where A is a posi... View the full answer