engineering math (surface integral)
engineering math (surface integral) QUESTION 8 Evaluate the surface integral (J 6(x, y) ds where o...
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 (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 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 =
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...
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.
(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...
Evaluate the surface integral lis(r,y,z) (x, y, z) ds where f(x, y, z) = x + y + z and o is the is the surface of the cube defined by the inequalities 0 < x < 5,0 Sy < 5 and 0 <3 < 5. [Hint: integrate over each face separately.] 1 f(x, y, z) ds =
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The value of the surface integral is (Type an exact answers, using t as needed.) Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. f(xyz) = 4x, where S is the cylinder X + z2-25, 0 ys2 The value of the surface integral is (Type exact answers, using T as needed.) Find the area of the following surface using the given explicit description of the surface. The cone z2 = (x2 +y2) , for Oszs8 Set up the surface integral for the given function over the given surface S as a...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...