Evaluate the integral. 3. Sss (xz – yz)ds; where S is portion of the plane in...
Evaluate the surface integral. SSs yz ds S is the part of the plane x + y + z = 9 that lies in the first octant. 243V3
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, double integral F*ds, where F = [(e^x)cos(yz), (x^2)y, (z^2)(e^2x)] and S is a part of the cylinder 4y^2 + z^2 =4 that lies above the xy plane and between x=0 and x=2 with upward orientation (oriented in the direction of the positive z-axis). ASAP PLEASE
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 following integral, ∫ ∫ S z dS, where S is the part of the sphere x2 + y2 + z2 = 16 that lies above the cone z = √ 3 √ x2 + y2 . Problem #6: Evaluate the following integral where S is the part of the sphere x2+y2 + z -y2 16 that lies above the cone z = 3Vx+ Enter your answer symbolically, as in these examples pi/4 Problem #6: Problem #6: Evaluate the...
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 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
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...
(10 pts) Evaluate the surface integral | F. ndo where F = x'i+y’j + zk and S is the portion of the plane z = y + 1 that lies inside the cylinder 12 + y2 = 1.