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Evaluate the surface integral. SSs yz ds S is the part of the plane x +...
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 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
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 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) = xzey i − xzey j + z k S is the part of the plane x + y + z = 7 in the first octant and has upward orientation.
Evaluate the surface integral SSS 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) = xi - zj + y k S is the part of the sphere x2 + y2 + z2 = 36 in the first octant, with orientation toward the origin.
Evaluate the surface integral s«w.vz) as where f(x, y, z) = x - y - zand o is the portion of the plane x + y = 1 in the first octant between 2 = 2 and 2 = 3. Enter the exact answer. f(x, y, z) ds = ? Edit 46.9.2) ds =
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
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
(1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate the flux integral of the vector field F 2i + j + 3k across the surface S (with N being the unit upward vector normal to the plane). B.I 48 C. I 72 E. 1 24 (1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate...
2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal. 2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal.