Consider F and C below. F(x, y, z) = yze?i + e'?j + xyek, C: r(t)...
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 10z) k C is the line segment from (3, 0, -3) to (4, 4, 1) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate [s vf. dr along the given 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.
1. (25 pts] Let F(x, y, z) = (2xy4 +25)i + (4.x²y3 + 2yz3)j + (5x24 + 3y2 -2)k and let C be the curve given parametrically by r(t) = (3t+1)i + t?j + 5tk for 0 <t<1. Evaluate the line integral [F F. dr
[25 pts] Let F(x, y, z) = (2xy4 + 25)i + (4x´y3 + 2yz3)j + (5x24 + 3y2-2)k and let C be the curve given parametrically by r(t) = (3t+1)i + t?j + 5tk for 0 <t< 1. Evaluate the line integral F. dr
(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 =...
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), ?) ,
Complete the first question and fill in the missing blank for
the other thank you!
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 182) k C is the line segment from (3, 0, -3) to (5, 5, 3) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate Vf. dr along the given curve C. Therefore, the work done is as...
Letf(r, y. z).(2xve, + yen.x,z, + xe".3x, yt, +cos:). a. Please find (2y+ye 5. С:/(r)-(cost.sin 1,1). Osis". dy b. Please to prove that F is a conservative vector field: ye". c. Please find J2xye d. Please find the potential function fx, y, z) such that F Vf e. Use the part (d) to evaluate F dr along the given curve C. f. Please find curlF g. Please find curlF
Letf(r, y. z).(2xve, + yen.x,z, + xe".3x, yt, +cos:). a. Please...
1. (25 pts] Let F(x, y, z) = (2xy+ + 25)i + (4x²y3 + 2yz3)j + (5x24 + 3y2z2)k and let C be the curve given parametrically by r(t) = (3t+1)i + tºj + 5tk for 0 <t<1. Evaluate the line integral Sa Spa
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...