Evaluate the surface integralG(x, y, z) ds G(x, y, z) (x2 +y')z; S that portion of...
Could you do number 4 please. Thanks 1-8 Evaluate the surface integral s. f(x, y, z) ds Vx2ty2 -vr+) 1. f(x, y, z) Z2; ơ is the portion of the cone z between the planes z 1 and z 2 1 2. f(x, y, z) xy; ơ is the portion of the plane x + y + z lying in the first octant. 3. f(x, y, z) x2y; a is the portion of the cylinder x2z2 1 between the planes...
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 S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 36 in the first octant, with orientation toward the origin
(1 point) Evaluate the surface integral / F. dS where F = (-4x, 3z, – 3y) and S is the part of the sphere x2 + y2 + z2 = 16 in the first octant, with orientation toward the origin. SIsFdS =
(8 points) Evaluate the surface integral SF. dS where F = (1, 32, 3y) and S is the part of the sphere x2 + y2 + z2 = 4 in the first octant, with orientation toward the origin. SSSF. ds
where g is a function of one variable 16. Suppose that f(x,y,z)= g(V x2 + y2 + such that g(3) = 4. Evaluate ſyf(x,y,z)ds' where S is the sphere x² + y2 +z2 =9.
6. Use the Divergence Theorem to evaluate SSF. ds, where Ể(x, y, z) = (x/x2 + y2 + z2 , yvx2 + y2 + z2 , z7 x2 + y2 + z2 ) and S consists of the hemisphere z V1 – x2 - y2 and the disk x2 + y2 = 1 in the xy-plane.
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
7. Evaluate z ds. where s is the surface z-= x2 + y2, x2 + y2-1. 7. Evaluate z ds. where s is the surface z-= x2 + y2, x2 + y2-1.
Evaluate the surface integral ∫∫sF·ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y,z) = xi - zj +yk S is the part of the sphere x2 + y2 + z2 = 16 in the first octant, with orientation toward the origin.