GIRNE AMERICAN UNIVERSITY Evaluate ScF. dr where F(x, y, z) = zi + x2j + yk...
(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
Evaluate ScF. dr where F(x, y) = xy?i + xyºj and C is the polygonal path from (0,0) to (1,0) to (0,1) to (0,0) Select one: O a. 30 1 O b. 35 c. 110 O d. - 3
Use Stoke's Theorem to evaluate ScF. dr, where F(x, y, z) = -xzzi + y2zj + zºk and C is the curve of intersection of the planez = 1 – X – Y and the cylinder x2 + y2 = 1, oriented counterclockwise as viewed from above.
Evaluate Scf(x, y)dS where C is the curve y = x3 for 0 SX S1 and the surface is f(x, y) = V1 + 9xy Select one: 15 a. 7 IS b. 13 5 13 O c. 1 7 O d. d. 1 14 5
What is the value of ScF. Tds, where F(x, y, z) = y² i + 2xzj + 6xk and C is the straight-line segment r(t) = ti + tj + tk, 0 <t<1 from (0,0,0) to (1,1,1)?
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = (-y+z)i + (x – z)j + (x – y)k. S is the surface z = V1 – 22 – y2, and C is the boundary of S with counterclockwise orientation (from above).
12) Let F(x,y) = yi + x2j. Evaluate Sc F. dr for the parabolic curve C: r(t) = ti + (4t-t?) Osts 3.
F. dr Find a function of such that of 8 and then evaluate where F(x, y) = < 3 + 2kg", 2y) and C is any smooth curve from (-2, 1) to (1,2).
3. Use Stokes' Theorem to evaluate [ſcurl Ē. d5 where F(x, y, z)= x?y?zi + sin(xyz)ị + xyzk, o is the portion of the cone y² = x² +z? that lies between the planes y=0) and y = 3, oriented in the direction of the positive y-axis. [2187 1/4]
8 points each 1. F is a conservative vector field. Evaluate ScF. dr where F =< 2xy3-4, 3x2y224, 4x^y323 > and C is the curve beginning at (3, 0, 5) and ending at (3, 2, -1)