This question has several parts be F. dr as a surface integral. You will use Stokes'...
DETAILS 3. [2/4 Points) Consider the given vector field. F(x, y, z) = (e", ely, exy?) (a) Find the curl of the vector field. - yzelyz lazenz curl Fe (b) Find the divergence of the vector field. div F = ertxely tuxely F. dr This question has several pa You will use Stokes' Theorem to rewrite the integral and C is the boundary of the plane 5x+3y +z = 1 in the fir F-(1,2-2, 2-3v7) oriented counterclockwise as viewed from...
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = xyzi+yj + zk. S is the surface 3x + 4y + 2z = 12 in the first octant, and is the boundary of S with counterclockwise orientation (from above).
Evaluate the line integral - dr by evaluating the surface integral in Stokes Theorem with an appropriate choice of metal Close counterdeckwite orientation when viewed from above С F-6²-82-x².7² -2²) C is the boundary of the square Ix 13. lys 13 in the plane 2 #0 Rewrite the given in integral as a | as a surface integral fro-SSO ds C 5 Evaluate the integral $r..-Type an exact answer
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
Use Stokes' Theorem to evaluate the line integral $cF.dr, where F(x, y, z) = xyzi + yj + zk, Sis the surface 3x + 4y + 2z = 12 in the first octant, and is the boundary of S with counterclockwise orientation (from above).
Problem 6 Using Stokes' Theorem, we equate F dr curl F dA. Find curl F- PreviousS us Problem ListNext Noting that the surface is given by (1 point) Calculate the circulation, Fdr7in z - 16-x2 - y2, find two ways, directly and using Stokes' Theorem. dA The vector field F = 6y1-6y and C is the boundary of S, the part of the surface dy dx With R giving the region in the xy-plane enclosed by the surface, this gives...
Use Stokes' Theorem to evaluate F. dr where Cis oriented counterclockwise as viewed from above. F(x, y, z) - xy + 27 + 6yk, C is the curve of intersection of the plane X + 2-1 and the cylinder + 9.
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e k and C is the circy4,z 5 oriented counterclockwise as viewed from above Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards The easiest surface to attach to this curve is the disk x2 + y2 < 4, z-5. Using this surface in Stokes' Theorem evaluate the following. F-dr = where sqrt(4-xA2) sqrt(4-x^2)...
Use the surface integral in Stokes' Theorem to calculate the circulation of the field F=x^2i+5xj+z^2k around the curve C: the ellipse 16x^2 + y^2 = 1 in the xy-plane, counterclockwise when viewed from above.