Evaluate the integral for the following data. F = [x - z, y - x,z-y], 5....
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
(,y,) dS, where f(,y,) = z'yz2 and S is the part ys 4 1. Parametrize, but do not evaluate, +y of the graph of z over the rectangle -2 S rs3 and 0 2. Parametrize, but do not evaluate, F.n dS, where F (y,-r,z) and S is the sphere of radius 2 centered at the origin. Math 224 3. Calculate le ayz dS where S is the part of the cone parametrized by 0sus1,0svs r(u, v)(ucos v, usin v, u),...
A B C Parametrize, but do not evaluate, //f(x, y, z) ds, where f(x, y, z) 2y22 and S is the part , where J(,y,) 3 3 and 0 Sys4 of the graph of z2 over the rectangle -2 s . Parametrize, but do not evaluate, F.n ds, where F (,-,z) and S is the sphere of radius 2 centered at the origin. Calculate JJs xyz dS where S is the part of the cone parametrized by r(u, u) (ucos...
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 integral Ms (x, y, z) ds over the surface o represented by the vector-valued function r (u, v). -; r(u, v) = 7 u cos vi+7 u sin vj + 7 u’ k (0 sus sin v, 0 SV ST) 9 f (x, y, z) = 49 + 4x2 + 4y2 Enter the exact answer. 144 f (x, y, z) dS = ? Edit 0 action Attornten of 1
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) , Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) ,
9. Evaluate the “vector valued” line integral 1.Podr Fodr where F(x, y, z) = (x, y, zy) TT and C is given by r(t) = (sint, cost, t), with N » 4. u sta
Evaluate the surface integral. 1 (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u - v, z = 1 + 2 + v, osus 6, Osvs 2.
Evaluate the surface integral. (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u – v, z = 1 + 2u + v, Osus 6, 0 SV 53. Is
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...