Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the 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
Evaluate the integral. 3. Sss (xz – yz)ds; where S is portion of the plane in R3 z = x + y + 2, that lies inside the cylinder x2 + y2 = 1.
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...
engineering math (surface integral) QUESTION 8 Evaluate the surface integral (J 6(x, y) ds where o is the portion of the surface -= x² + y2 below the plane == 2. ace integral (150, 1) ds whe
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
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
5. Evaluate the surface integral SL.F 45, where F(x, y, z) = ri, and S is the part of the paraboloid z = Ty-plane, oriented upward. -x2 – y? +1 above the
(1 point) Evaluate the surface integral || (3x yi – 3yzj + zxk) · dS. JJ s . Where S is the part of the paraboloid z = 9 – x2 - y2 that lies above the square 0 < x < 2, 0 < y < 1, and has upward orientation. X2 / 2 (3xyi – 3yzj + zxk) · dS = JJS 9-x^2-y^2 Σ dy dx J xi Jyi where M M O-ON x1 = M M Evaluate...
using this formula 2. Evaluate the surface integral F. dS, where F(x, y, z) = xi+yj+zk is taken over the paraboloid z=1 – x2 - y2, z > 0. SA errom bove de SS (-P (- Puerto Q + R) dA dy
(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