12) Let F(x,y) = yi + x2j. Evaluate Sc F. dr for the parabolic curve C:...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
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), ?) ,
15. Let F(z,y)- F dr where C is any positively-oriented Jordan curve that encloses the origin Evaluate 15. Let F(z,y)- F dr where C is any positively-oriented Jordan curve that encloses the origin Evaluate
Evaluate Sc f(x,y)ds where is the curve y = x for 0 < x < 1 and the surface is f(x,y) = 1 + 9xy Select one: 14 a. 5 O a. V O b. O c. 18 13 O d. 1
Suppose f(x,y) is such that V f is continuous everywhere. Let C be the smooth curve given by F(t) = (cos(t), cos(t) sin(t)) for 0 <t< 7/4. Suppose we know that f(0, 1) = 3, $(1,0) = 7, f (VE) = 2, 2' 2 Use this information to find Sc Vf. dr. Show all work and expain your reasoning.
(1 point) Evaluate the line integral ScF. dr, where F(x, y, z) = -4xi – 4yj + 5zk and C is given by the vector function r(t) = (sin t, cost, t), osts 31/2. 4
GIRNE AMERICAN UNIVERSITY Evaluate ScF. dr where F(x, y, z) = zi + x2j + yk and C is the line segment from (1,2, 3) to (4,3, 2) of Select one: O a. 12 O b. 13 O c. 11 O d. 10 Ne
Let F(x, y, z) be the gradient vector field of f(x, y, z) = exyz , let C be the curve of the intersection of the plane y + z = 2 and the cylinder x2 + y2 = 1, oriented counterclockwise, evaluate Sc F. dr. OT O -TT O None of the above. 00
Use Stokes' Theorem to find SC F. dr where F(x,y,z) = (-y, x,x) and C is the curve of intersection of the plane y = 2 and the paraboloid y + x2 + z2 = 6. Show all work. Please select file(s) Select file(s)
please show all work Use Stokes' Theorem to evaluate Sc F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyl +22+ 4yk, C is the curve of intersection of the plane X + 2 = 10 and the cylinder x2 + y2 - 36.