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Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0, 1) to (e, 2). 1. I2e3 +1 2. I2e - 1 4. Ie -4 5...
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C...
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), ?) ,
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z =...
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'...
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
Et F(r, v) (3z2e* + sec z tan z,ze - 90y*). (a) Show that F is a conservative. (b) Find a functio...
et F(r, v) (3z2e* + sec z tan z,ze - 90y*). (a) Show that F is a conservative. (b) Find a function f (potential function) show that F Vf. (c) Use above result to evaluate JeFdr, where C is a smooth curve that begin at the point (2, 1) and ends at (0, 3). (cost, sint) from -2 to t = 줄 particle that moves along the curve. (Write the value of work done without evaluating d) Find the work...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evalu...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
(2) For the vector field f 2z(ri yi)(22)k use the definition of line integral to evaluate the line integral J f.dr along the helical path r-costi + sintj+tk, 0St (3) You are given that the vector fie...
(2) For the vector field f 2z(ri yi)(22)k use the definition of line integral to evaluate the line integral J f.dr along the helical path r-costi + sintj+tk, 0St (3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2
(2) For the vector field f 2z(ri yi)(22)k use the definition of line integral to evaluate the line integral J f.dr along...
Let F(x,y,z) = <2y2z, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative,...
Let F(x,y,z) = <2y2z, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative, find a function f such that F = Vf and f(1,2,1)= 8. (b) Using the result of part(a), evaluate the line integral of F along the following curve C from (0, 0, 0) to (3.9, 1.4, 2.6). y2 + x4z3 + 2xy(x3 + y4 + 24)1/3 = K ; K is a constant Answer: Next page
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xzey i − xzey j + z k S is the part of the plane x + y + z = 7 in the first octant and has upward orientation.
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 36 in the first octant, with orientation toward the origin
4:L1-2 Consider the vector field F on Rgiven by () F(x, y) 0 and the curve...
4:L1-2 Consider the vector field F on Rgiven by () F(x, y) 0 and the curve c: (0,1) + R2 with 2++ + cos(t) Compute the line integral de) = ( Cand cele). \<F1ds>. { <F | do>- <insert a positive integer> Ono For partial credit, fill in the following. You can use sage-syntax, or simply write text. Note that not all ways of solving this problem depend on all fields below. Is the vector field conservative? Oyes If the...
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), ?) ,
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
et F(r, v) (3z2e* + sec z tan z,ze - 90y*). (a) Show that F is a conservative. (b) Find a function f (potential function) show that F Vf. (c) Use above result to evaluate JeFdr, where C is a smooth curve that begin at the point (2, 1) and ends at (0, 3). (cost, sint) from -2 to t = 줄 particle that moves along the curve. (Write the value of work done without evaluating d) Find the work...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
(2) For the vector field f 2z(ri yi)(22)k use the definition of line integral to evaluate the line integral J f.dr along the helical path r-costi + sintj+tk, 0St (3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2
(2) For the vector field f 2z(ri yi)(22)k use the definition of line integral to evaluate the line integral J f.dr along...
Let F(x,y,z) = <2y2z, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative, find a function f such that F = Vf and f(1,2,1)= 8. (b) Using the result of part(a), evaluate the line integral of F along the following curve C from (0, 0, 0) to (3.9, 1.4, 2.6). y2 + x4z3 + 2xy(x3 + y4 + 24)1/3 = K ; K is a constant Answer: Next page
4:L1-2 Consider the vector field F on Rgiven by () F(x, y) 0 and the curve c: (0,1) + R2 with 2++ + cos(t) Compute the line integral de) = ( Cand cele). \<F1ds>. { <F | do>- <insert a positive integer> Ono For partial credit, fill in the following. You can use sage-syntax, or simply write text. Note that not all ways of solving this problem depend on all fields below. Is the vector field conservative? Oyes If the...
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