Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (−4, 1), (−4, −2),...
Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (−4, 1), (−4, −2), (2, −1), (2, 6), and back to (−4, 1), in that order. Use Green's theorem to evaluate the following integral. C (2xy) dx + (xy^2) dy
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Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (−4, 1), (−4, −2),...
Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the...
Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (0, 0, 0), (2, 1, 5), (1, 1, 3), and back to the origin, in that order. Use Stokes' theorem to evaluate the integral: (Use symbolic notation and fractions where needed.) (xyz) dx + (3xy) dy + (x) dz = D .
please solve all thank you so much :) Let C be the curve consisting of line...
please solve all thank you so
much :)
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...
(a) Let S be the area of a bounded and closed region D with boundary дD of a smooth and simple cl...
(a) Let S be the area of a bounded and closed region D with boundary дD of a smooth and simple closed curve, show that S Jlxy -ydx by Green's Theorem. (Hint: Let P--yandQ x) (b) Let D = {(x,y) 1} be an ellipse, compute the area of D a2 b2 (c) Let L be the upper half from point A(a, 0) to point B(-a, 0) along the elliptical boundary, compute line integral I(e* siny - my)dx + (e* cos...
Suppose is a closed curve in the plane and that -Y dr + 2? + y2...
Suppose is a closed curve in the plane and that -Y dr + 2? + y2 2 dy = 671 z? + y2 How many self-intersection points must have, at least? By "self-intersection point", I mean a point where the curve intersects itself other than its endpoints. For example, a simple closed curve has zero self-intersection points, and a figure 8 has one self-intersection point. Hint: If a curve has self-intersection points, then it can be divided up into a...
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to th...
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the curve from above. point in the anti-clockwise direction when viewed Calculate the line integral (e (e sin y+ 4) dy+(e(cos z+ sin z)+ay) dz. cos x2yz) dx +
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the...
number 6. to udestyoRe phenomena ren is the Key to understanding these ty ercises 1. Let...
number 6.
to udestyoRe phenomena ren is the Key to understanding these ty ercises 1. Let S be the portion of the plane 2x + 3y+ z Let S be the portion of the surface z-x2 +y2 lyin between the points (0, 0, 0). (2, 0, 4). (0, 2, 4), and (2, 2, 8). Find parameterizations for both the surface and its boundary aS. Be sure that their respective orientations are compatible with Stokes theorem. 5 lying 2. between the...
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space...
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space given by F(x, y, z) xy-plan described by x2 + y2 < 4, z = 0; and let S2 be the upper half of the paraboloid given by z 4 y2, z 2 0. Both Si and S2 are oriented upwards. Let E be the solid region enclosed by S1 and S2 (a) Evaluate the flux integral FdS (b) Calculate div F div F...
10. [8 points] Use Green's Theorem to evaluate the line integral Sexy dx + (x2 +...
10. [8 points] Use Green's Theorem to evaluate the line integral Sexy dx + (x2 + y) dy, where the closed curve C determined by y=x2 and y - =2 between (-1,1) and (2, 4). Sketch the curve and the region enclosed by the curve.
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector...
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 4 sin(y)...
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 4 sin(y) dx + 4x cos(y) dy C is the ellipse x2 + xy + y2 = 49 Ic
Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (0, 0, 0), (2, 1, 5), (1, 1, 3), and back to the origin, in that order. Use Stokes' theorem to evaluate the integral: (Use symbolic notation and fractions where needed.) (xyz) dx + (3xy) dy + (x) dz = D .
please solve all thank you so
much :)
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...
(a) Let S be the area of a bounded and closed region D with boundary дD of a smooth and simple closed curve, show that S Jlxy -ydx by Green's Theorem. (Hint: Let P--yandQ x) (b) Let D = {(x,y) 1} be an ellipse, compute the area of D a2 b2 (c) Let L be the upper half from point A(a, 0) to point B(-a, 0) along the elliptical boundary, compute line integral I(e* siny - my)dx + (e* cos...
Suppose is a closed curve in the plane and that -Y dr + 2? + y2 2 dy = 671 z? + y2 How many self-intersection points must have, at least? By "self-intersection point", I mean a point where the curve intersects itself other than its endpoints. For example, a simple closed curve has zero self-intersection points, and a figure 8 has one self-intersection point. Hint: If a curve has self-intersection points, then it can be divided up into a...
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the curve from above. point in the anti-clockwise direction when viewed Calculate the line integral (e (e sin y+ 4) dy+(e(cos z+ sin z)+ay) dz. cos x2yz) dx +
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the...
number 6.
to udestyoRe phenomena ren is the Key to understanding these ty ercises 1. Let S be the portion of the plane 2x + 3y+ z Let S be the portion of the surface z-x2 +y2 lyin between the points (0, 0, 0). (2, 0, 4). (0, 2, 4), and (2, 2, 8). Find parameterizations for both the surface and its boundary aS. Be sure that their respective orientations are compatible with Stokes theorem. 5 lying 2. between the...
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space given by F(x, y, z) xy-plan described by x2 + y2 < 4, z = 0; and let S2 be the upper half of the paraboloid given by z 4 y2, z 2 0. Both Si and S2 are oriented upwards. Let E be the solid region enclosed by S1 and S2 (a) Evaluate the flux integral FdS (b) Calculate div F div F...
10. [8 points] Use Green's Theorem to evaluate the line integral Sexy dx + (x2 + y) dy, where the closed curve C determined by y=x2 and y - =2 between (-1,1) and (2, 4). Sketch the curve and the region enclosed by the curve.
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 4 sin(y) dx + 4x cos(y) dy C is the ellipse x2 + xy + y2 = 49 Ic
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