Evaluate 1 dS where s is the surface z = 3 inside the cylinder x2 + y2-1. B.π C. 3/2 D. 2T E. 3π
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.
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π 9. Let Q be the solid bounded by the cylinder x2 + y2...
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
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f,...
Evaluate the integral, where E is the region that lies inside the cylinder x2 + y2 = 4 and between the planes z = -1 and z = 0. Use cylindrical coordinates. SSSE V.x2 + y2 DV =
Evaluate z) ds, where S is the intersection of the plane z=4-y with the solid cylinder x2 + y2 33. 8. 127211 ob.8V21 C. None of these O d. 4√3 a e. 1231
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.
Evaluate the surface integral. 1. (x2+42+7) o ds S is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 and 2 = 2, together with its top and bottom disks
Evaluate the following integral, ∫ ∫ S (x2 + y2 + z2) dS, where S is the part of the cylinder x2 + y2 = 25 between the planes z = 0 and z = 9, together with its top and bottom disks
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...