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7. Evaluate SS(0,0,x). nds where S is the surface of the cone z= V x² +...
SS zds, s 0:3 evaluate the surface integral where is the cone z = V x² + y2 between the xy-plone and le colid s cut z = 2.
7. Evaluate the circulation integral [/s<= x F) .nds where F(x, y, z) = (x + 3,4+2,2 + y) and S is part of the upper part of the sphere r2 + y2 + 2+ = 25 with 3 <=55(you may use any theorem you find helpful).
4. Evaluate the Surface Integral [f(r,y,0)nds , where S is the part of the surface z-Vx+y* below z-1, and i is the unit outer normal to S with negative z- component. 4. Evaluate the Surface Integral [f(r,y,0)nds , where S is the part of the surface z-Vx+y* below z-1, and i is the unit outer normal to S with negative z- component.
Evaluate S Ss y2z2 ds, where S is the part of the cone z = vx2 + y2 that lies between the planes z = 1 and 2 = 2.
1. Evaluate the surface Integrals using Divergence (Gauss') Theorem. a) ff(xyi +2k)ndS where S is the surface enclosing the volume in the first octant bounded by the planes z-O, y-x, y-2x, x + y+1-6 and n İs the unit outer normal to S. b) sffex.y,22)idS, where S is the surface bounding the volume defined by the surfaces z-2x2 +y, y +x2-3, z-0 and n İs the unit outer normal to S. o_ ffyi+y'j+zykids, where S is the ellipsoid.x^+-1 and iis...
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
Let F(x,y,z) = 4i – 3j + 5k and S be the surface defined by z= x2 + y2 and 22 + y2 < 4. Evaluate SJ, F. nds, where n is the upward unit normal vector.
Evaluate Syzeds, where s is the part of the cone z= x² + y2 that lies between the planes Z=1 and Z=2
2. Let I be the surface of the cone z = V x2 + y2 (without the top) between planes z = 0 and z = 2. Let F =< x,y,z2 >. Calculate the upward directed flux SS FdS (a) Using the Divergence Theorem. (10 points) (b) Without using the Divergence Theorem. (20 points)
2. Evaluate 1,(1,0, 2) . ds, where s is the cone z = VE4y2 with 0 < z < 2, Upward 1,0,2) ds, where S is the pointing normal. 3. Use a surface integral to find the area of the region of the plane z2y +3 with 2. Evaluate 1,(1,0, 2) . ds, where s is the cone z = VE4y2 with 0