Evaluate the surface integral lis(r,y,z) (x, y, z) ds where f(x, y, z) = x +...
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...
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
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 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, 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
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).)...
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
4. Evaluate the Surface Integral [f(r,y,0)nds , where S is the part of the surface z-Vx+y* below z-1, and i is the unit outer normal to S with negative z- component. 4. Evaluate the Surface Integral [f(r,y,0)nds , where S is the part of the surface z-Vx+y* below z-1, and i is the unit outer normal to S with negative z- component.
Evaluate the integral: dzdrdy where B is the cylinder over the rectangular region R {(x,y) E R2:-1 1,-2y2) sin z sy and above by the sr of the , bounded ethe surface 12 уг 2- face of elliptical paraboloid 37 42081 Evaluate the integral: dzdrdy where B is the cylinder over the rectangular region R {(x,y) E R2:-1 1,-2y2) sin z sy and above by the sr of the , bounded ethe surface 12 уг 2- face of elliptical paraboloid...