Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S h...
Verify Stokes' Theorem by evaluating the line integral and the double surface integral. Assume that the surface has an upward orientation. (a) F(x, y, z)= x’i + y²j+z?k; o is the portion of the cone below the plane z=l. (b) 7 (x, y, z)=(z - y){ +(z+x) ș- (x + y)k; o is the portion of the paraboloid z=9-r? - y2 above the xy-plane. [0, 187]
10. Stokes' Theorem and Surface Integrals of Vector Fields a. Stokes' Theorem: F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y?». Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) e. Use Stokes' Theorem to computec F dr 10. Stokes' Theorem and Surface Integrals...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi + 3yj + xk and the surface S the part of the paraboloid Z-5-x2-y2 that lies above the plane z 1, oriented upwards. / curl F diS To verify Stokes' Theorem we will compute the expression on each side. First compute curl F <0.3+2%-22> curl F - ds - where y1 curl F ds- Now compute /F dr The boundary curve C...
please answer the following question so a beginner can understand. 5.3 Surface integral of vector fields 5.4 Stokes' Theorem C simple closed, positively oriented w.r.t. S 5 5.5 Divergence Theorem S is outward oriented boundary of E, Example 8. Let D be the portion of z = 1-x2-y2 inside x2 + y2-1, oriented up. F-yi+zj-xk, compute JaF -ds. 5.3 Surface integral of vector fields 5.4 Stokes' Theorem C simple closed, positively oriented w.r.t. S 5 5.5 Divergence Theorem S is...
10. Stokes Theorem and Surface Integrals of Vector Fields a Stokes Theorem:J F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y, Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)ーーーーーーーーーーーーー Compute N(u,v) e. Use Stokes' Theorem to compute Jc F dr 10. Stokes Theorem and Surface...
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...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 3yd-2ǐ + 2xk and the surface S the part of the paraboloid z = 20-x2-y2 that lies above the plane z = 4, oriented upwards. To verify Stokes' Theorem we will compute the expression on each side. First computel curl F dS curl F- curl F. dS- EEdy di where curl F dS- Now compute F dr The boundary curve C of the...
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a 3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
Verify that Stokes' Theorem is true for the vector field Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ zj + xkand the surface S the hemisphere x2 + y2 + z2-25, y > 0oriented in the direction of the positive y- axis To verify Stokes' Theorem we will compute the expression on each side. First compute curl F dS curl F The surface S can be parametrized by S(s, t) -...
Verify Stokes’ Theorem if the surface S is the portion of the paraboloid z = 4 − x2 − y2 for which z ≥ 0 and F(x,y,z) = 2zi+3xj +5yk.