3. Suppose that C is the oriented curve consisting of the line segment from origin to...
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Let C be the curve consisting of line segments from (0, 0) to (3, 3) to (0, 3) and back to (0,0). Use Green's theorem to find the value of [ xy dx + xy dx + y2 + 3 dy. Use Green's theorem to evaluate line integral fc2x e2x sin(2y) dx + 2x cos(2) dy, where is ellipse 16(x - 3)2 + 9(y – 5)2 = 144 oriented counterclockwise. Use Green's...
2. Let C be the line segment from (0,5,0) to (2,0,-1). Calculate S (x²+z?)dx + (x2 + y)dy + (3x – 2y)dz.
Evaluate the line integral. fr de x² dx + y²dy, where C is the arc of the circle x2 + y2 = 4 from (2,0) to (0,2) followed by the line segment from (0, 2) to (4,3).
(d) The line integral [(x+y?)dx + (x2 + 2xy)dy, where the positively oriented curve C is the boundary of the region in the first quadrant determined by the graphs of x=0, y=x2 and y=1, can be converted to A 2xdydx 0 0 BJ 2 xdxdy 0 0 С -2x)dyda 00 D none of the above (e) Consider finding the maximum and minimum values of the function f(x, y) = x + y2 - 4x + 4y subject to the constraint...
Evaluate the integral ∮CF⋅dr for F=(5x2y)i+(2x2−5xy2)j on the
curve C consisting of the x-axis from x=0 to x=3, the arc of the
circle x2+y2=9 up to the line y=x, and the
line y=xdown to the origin. ∮CF⋅dr=
Evaluate the integral h. F . dr for F = (5x2 y)i + (2x2-5yj on the curve C consisting of the x-axis from x=0 tox-3, the arc of the circle x2 + y2-9 up to the line y=x, and the line y=xdown to...
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Let C be the closed curve consisting of two pieces. One piece is the upper-half circle of radius 3, centered at the origin, oriented counter-clockwise. The other piece is the horizontal line segment from (-3,0) to (3,0). Evaluate the line integral $ (x2 + y2)dx + (6xy—y?)dy = с (-3,0) (3,0) O 36 O 72 O 31 91/2 The level set of f(x,y) = 12 is a...
Use Green's Theorem to evaluate the line integral along the given positively oriented curve I = Sc (2y + 7eV*)dx + (3x + cos(y2))dy, where the curve C is the boundary of the region enclosed by the parabolas y = 9x2 and x = y2
(1 point) Use Green's Theorem to evaluate the line integral along the given postively oriented curve. 1 = [ (2y + 7eva)dx + (3x + cos(y?))dy C is the boundary of the region enclosed by the parabolas y = 7c and x = yº
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
Evaluate xy dx + (x+y)dy along the curve y=2x? from ( - 3,18) to (-2,8). с | xy dx +(x+y)dy = [ С (Type an integer or a simplified fraction.)