The vector field-mathbf{ h } (x,y)-2xisin(y)Imathbf{ İ } + gradient of the function f(x.y)-x 2lsin(y)te yf(a, y)-xsin(y) e. Evaluate the following with justification: Part a: The line integral of h o...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) , Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) ,
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line integral along the following paranie trized curves. G: gradient of any function f(x, y). Horizontal E vertical - Ellipse (9,14) (7,11) (13,7) ii) show that f(x, y) is not equal to the C, (579)
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line integral along the following paranie trized curves. G: gradient of any function f(x, y). Horizontal E vertical - Ellipse (9,14) (7,11) (13,7) ii) show that f(x, y) is not equal to the C, (579)
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...
Let F = (P,Q) be the vector field defined by -x+y . P(x,y) = 22, (x, y) + (0,0) 0, (x, y) = (0,0) Q(x,y) = (x, y) + (0,0) x2+y2; 10,(x, y) = (0,0). (a) Show that F is a gradient vector field in R2 \ {y = 0}. (b) Letting D = {2:2020 + y2020 < 1}, compute the line integral Sap P dx + Q dy in the counter-clockwise direction. (c) Does your calculation in part (b)...
Let F = (P,Q) be the vector field defined by P(x,y) ity, (1, y) = (0,0) 10, (x,y) = (0,0) Q(x, y) = -Ity. (x, y) = (0,0) 10, (x, y) = (0,0). (a) (3 points) Show that F is a gradient vector field in RP \ {y = 0}. (b) (4 points) Letting D = {2:2020 + y2020 < 1}, compute the line integral Sap P dx +Qdy in the counter-clockwise direction. (c) (1 point) Does your calculation in...
Evaluate the line integral of the function f(x,y)= (x+y2)/(sqrt(1+x2)) over the curve C: y=x^2/2 ; from (1,1/2) to (0,0)
Use (part A) line integral directly then use (part B) Stokes' Theorem 10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C is the unit circle in the plane z (a) 67 (d) 12m 3. (b) TT (e) None of these (c) 3 TT 10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C...
(1 point) Consider the vector field F(x, y, z) = (2z + 3y)i + (2z + 3x)j + (2y + 2x)k. a) Find a function f such that F = Vf and f(0,0,0) = 0. f(x, y, z) = b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral / F. dr. (1 point) Verify that F = V and evaluate the line integral of F over the given path: F =...