In problems 3-5 evaluate ∫?⃗∙??⃗? using Stokes’ theorem. In each case ? is oriented counterclockwise when viewed from above.
In problems 3-5 evaluate ∫?⃗∙??⃗? using Stokes’ theorem. In each case ? is oriented counterclockwise when...
Use Stokes' Theorem to evaluate les F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y + z2)j + (z + x2)k, C is the triangle with vertices (3, 0, 0), (0, 3,0), and (0, 0, 3). Need Help? Read it Watch It Master It Talk to a Tutor
#10 Ja Problems 6 through 10, use Stokes' theorem to evaluate F.Tds. OF=3yi - 2xj + 3yk; C is the circle x2 + y2 = 9, Z = 4. oriented counterclockwise as viewed from above. 1.F=2zi+xj+3yk; C is the ellipse in which the plane z = x meets the cylinder x? + y2 = 4, oriented counterclockwise as viewed from above. & F= yi+zj+xk; C is the boundary of the triangle with ver- tices (0,0,0), (2,0,0), and (0, 2, 2),...
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 3xzj + exyk, C is the circle x2 + y2 = 16, z = 8.
Use Stokes' Theorem to evaluate integral_C F middot dr. C is oriented counterclockwise as viewed from above. F(x, y, z) = yz i + 8xz j + e^xy k C is the circle x^2 + y^2 = 1, z = 2.
Stokes' Theorem Verify Stokes' Theorem by evaluating each side of the equation in the theorem Here, F (x2 y, y2 - z2,z2 -x2) S is the plane x + y z 1 in the first octant, oriented with upward pointing normal vector, and y is the boundary of S oriented counterclockwise when seen from above. State Stokes' Theorem in its entirety Sketch the surface S and curve, y Explain in detail how all the conditions of the hypothesis of the...
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.
please show all work Use Stokes' Theorem to evaluate Sc F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyl +22+ 4yk, C is the curve of intersection of the plane X + 2 = 10 and the cylinder x2 + y2 - 36.
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)...
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...
Use Stokes' Theorem to evaluate fF.dr where F = (x +92) i + (1x + y)j + (2y = z)k and C is the curve of intersection of the plane x + 3y +z = 12 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.)