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...
-. (15 pts.) Let S is the first-octant portion of the plane 2x + y +z = 4. Evaluate the surface integral SSE (2y2 + 2yz) ds.
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...
Let Surface S be that portion of the cylinder x2 + y2 = 9, which lies between the planes z = y and z = 6. a.) Sketch the Surface S. b.) Parametrize the Surface S. c.) Evaluate the following Surface Integral: ∫∫(y-z)dS
Let S be the union of the following: • The portion of the cylinder x ^2 + y ^2 = 4 where x ≥ 0, bounded between the planes z = 0 and z = 2. • The rectangle −2 ≤ y ≤ 2, 0 ≤ z ≤ 2 in the yz-plane. Evaluate the integral Z Z S xz dS
Let S be the union of the following: • The portion of the cylinder x ^2 + y ^2 = 4 where x ≥ 0, bounded between the planes z = 0 and z = 2. • The rectangle −2 ≤ y ≤ 2, 0 ≤ z ≤ 2 in the yz-plane. Evaluate the integral Z Z S xz dS
Evaluate the surface integralG(x, y, z) ds G(x, y, z) (x2 +y')z; S that portion of the sphere x2 + y2 + z2-16 in the first octant eBook
5. (25 points) Let S be the union of the following: • The portion of the cylinder x2 + y² = 4 where x > 0, bounded between the planes z = 0 and z = 2 • The rectangle -2 SyS 2,0523 2 in the yz-plane. Evaluate the integral ads
Let Surface S be that portion of the paraboloid z = x2 + y2, which lies between the planes z = 4 and z = 25. Find the Area of S.
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,...