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...
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
help with #2 (2) Verify Stokes' theorem for where s is the portion of the surface of the cone z = VF+7 : 0 2, with normal n pointing z upward" (2) Verify Stokes' theorem for where s is the portion of the surface of the cone z = VF+7 : 0 2, with normal n pointing z upward"
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. f(xyz) = 4x, where S is the cylinder X + z2-25, 0 ys2 The value of the surface integral is (Type exact answers, using T as needed.) Find the area of the following surface using the given explicit description of the surface. The cone z2 = (x2 +y2) , for Oszs8 Set up the surface integral for the given function over the given surface S as a...
Provide correct answer Evaluate the surface integral Slo(x2 + y2 +42 ) ds where S is the part of the cone z = 4 - Vx2 + y2 above the z = 0 plane. The surface integral equals 271.62.pl
(14 points) Let F be the radial vector field Ft(z, y, z) =zi+w+sk And S be the surface of the cone shown at right parameterized by G(r,)-(rcos(0),r sin(0),6-3r) Write the integral F dS using an outward pointing normal in dS terms r and θ. This cone has an open bottom. . The integrand must be fully simplified » Do not evaluate the integral (14 points) Let F be the radial vector field Ft(z, y, z) =zi+w+sk And S be the...
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.
F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluate pointing out of the cylinder. 6-Let F(x, y,2)- yi- xj +zx°y?k. Evaluate (Vx F) . dS where S is the surface x2+y+32 - 1, z <0 oriented by the upward- pointing unit normal. F-dS where S is the cylinder x? +-2, 0 s y
1 point Let S be the portion of the sphere z2 + y2 +z2-4above the cone z-cVz2tr where c-1N3 Find the surface area of S Surface Area 2sqrt3 Evaluate the surface integral 1 point Let S be the portion of the sphere z2 + y2 +z2-4above the cone z-cVz2tr where c-1N3 Find the surface area of S Surface Area 2sqrt3 Evaluate the surface integral
Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2. Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2.