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Struggling with this! Please be clear with steps Thank you 5. (Section 16.3) F(x, y)= yi+(x+10y)j...
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.
(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...
please respond with explanations for each step. thank you Problem 4 Evaluate the line integrals (a) (10 points) y da 2ax dy, where C is the curve r(t) (2t + 1) i+ 3t2 j, 0t 1. (b) (10 points) (ryz) ds, where C is the line segment from the point (2, 1,0) to the point (4,3,6) (c) (10 points) F.dr,where F is the vector field F(x, y) = yi - rj and C is the curve given by r(t) t2i+...
9. The work done by the force F(x, y) (2at +e) i (4y in moving a particle -re from (0,0) to (1,1) along the curve y =x4 needs to be calculated. a. Show that F is a conservative vector field. b. Describe three different ways to calculate the work. Answer: 3 +1/e c. Calculate the work by a method of your choice.. a. Show that F=(y+yz) i + (x + 32 + xz) j +(9yz2 + y 1) k is...
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...
(a) Find the flux of the vector field F=yi-xjtk across the surface σ which is 4. x2 +y2 and below z the portion of z 4 and is oriented by the outward normal. _t7г (b) Use Stokes' Theorem to evaluate the line integral of J F.dr of F--уз ì_x3 j+(x+z)k where C is the clockwise path along the triangle with vertices (0,0,0). (1.0,0)and (1.i.o) aong the thiangle with(i) t) (a) Find the flux of the vector field F=yi-xjtk across 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), ?) ,
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
I lost in this I need help please thank you (NO NEED MORE INFORMATION BECAUSE IT IS A HW QUESTION This is how they ask) + 9) [26] Given F(x, y)= (4x’e' + 3x?y?)i + (x*e” + 2x’y+y’e”); , (state any theorems you use!) [4;8;6;4;4] (a) show that F is a conservative vector field. (b) find a potential function f for F. (c) evaluate ( F.di where C is the line segment from (3,1) to (4,2). (d) if the curve...
Please help! Question 5 25 (5.1) Sketch some vectors in the vector field given by F(r, y) 2ri + yj. (3) (5.2) Evaluate the line integral fe F dr, where F(r, y, 2) = (x + y)i + (y- 2)j+22k and C is given by the vector function r(t) = ti + #j+Pk, 0 <t<1 (4) costrt>, 0St<1 (5.3) Given F(r, y) = ryi + yj and C: r(t)=< t + singat, t (3) (a) Find a function f such...