Find the line integrals of F=3yi + 4xj + 2zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path Cy: r(t) = ti + tj + tk, Osts 1 b. The curved path Cz: r(t) = Osts1 c. The path C, UC, consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) (0,0,0) (1.1.1)
Find the work done by force F=3(sqrt)z i−3x j+(sqrt)y k, from (0,0,0) to (1,1,1) over each of the... Find the work done by force F=3(sqrt)z i−3x j+(sqrt)y k, from (0,0,0) to (1,1,1) over each of the following paths. C1 =ti +tj +tk, C2 =ti + t2j + t4k, and C3∪C4 c1=7/6 c2=-1/5 what is c3uc4?
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.
(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
4. Let F(x, y, z)=(уг cosz, 2y sinx + e2z,Zye2z). Find JeF . Tds, where C is the straight line going from (0,1, 1) to (5,3,2) 4. Let F(x, y, z)=(уг cosz, 2y sinx + e2z,Zye2z). Find JeF . Tds, where C is the straight line going from (0,1, 1) to (5,3,2)
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along...
please help with parts b and c! I do not understand how to find F. Thank you! 7. Find the line integral of F-(6x2-6x) i +6z j + k from (0,0,0) to (1,1,1) over each of the following paths in the accompanying figure. b.C2: r(t)-ti+12 j+14 k, 0sts1 c. C3UC4: the path consisting of the line segment from (0,0,0) to (1.1,0) followed by the segment from (1,1,0) to (1,1,1) a. The line integral of F over C1 is b. The...
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
5. z = +2 t2 (a) Find the arc-length of the curve C:r = V2t, y from the point 2 2 (0,0,0) to the point (V2, 1/2, 1/2). (b) Let C be the straight line segment from (0,0,0) to (1,1,1) in R3. Give a parametri- sation of C. I (c) Evaluate F. dr along the line segment C in Part (b), where F = ri + zrj + yk.
13. (10 points) (a): Find the line integral of f(x, y, z) = x+y+z over the straight-line segment from (1,2,3) to 0,-1,1). (b): Find the work done by F over the curve in the direction of increasing t, where F=< x2 + y, y2 +1, ze>>, r(t) =< cost, sint,t/27 >, 0<t<27.