(a) Set up a double integral for calculating the flux of the vector field F(x, y,...
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = z2k through the upper hemisphere of the sphere x2 + y2 + z2 = 4, oriented away from the origin. If necessary, enter P as rho, 8 as theta, and o as phi. B D Flux IT do de А A= B= C = D= (b) Evaluate the integral. Flux = F.dĀ= SI S
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
Setup Only 2. Flux calculations: Set up the double integral for Js F.dA using cylindrical, spherical or shadow method as appropriate. ) s is the conical face z = v x2 +V2 over the region r 2 on the xy-plane, oriented downwards. (c 2. Flux calculations: Set up the double integral for Js F.dA using cylindrical, spherical or shadow method as appropriate. ) s is the conical face z = v x2 +V2 over the region r 2 on the...
(1 point) Set up a double integral for calculating the flux of F -4xi + yj + zk through the part of the surface z =-2x-4y + 4 above the triangle in the xy-plane with vertices (0,0), (0,4), and (2,0), oriented upward. Instructions: Please enter the integrand in the first answer box. Depending on the order of integration you choose, enter dx and dy in either order into the second and third answer boxes with only one dx or dy...
(1 point) Evaluate the triple integral of f(x, y, z) = cos(x2 + y²) over the solid cylinder with height 2 and with base of radius 1 centered on the z axis at z = -2. Integral = 6pisin(4)
2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis defined by z2 +--4for-1SS3,oriented away from y-axis. F-3 (b) Sis given by z2 + y2 + z2-9and F-1n+zk. (c) S is the conical face -V+ over the region r S 2 on the zy-plane, oriented downwards. 2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis...
5. Surface integral of a vector field (10%) Consider the vector field F = fkır + ĉk2x. Evaluate the surface integral ſ F. ds over the surface of a closed cylinder about the z-axis specified by z = +3 and r = 2. (The cylinder has a height of 6 and a radius of 2.) The cylinder is illustrated below.
(1 point) Evaluate the triple integral of f(x, y, z) = cos(x2 + y2) over the solid cylinder with height 4 and with base of radius 2 centered on the z axis at z = -2. Integral
Set up a double integral for calculating the flux of F⃗ =4xi⃗ +yj⃗ +zk⃗ through the part of the surface z=−5x−5y+4 which lies above the triangle in the xy-plane with vertices (0,0), (0,2), and (2,0), oriented upward. Instructions: Please enter the integrand in the first answer box. Depending on the order of integration you choose, enter dx and dy in either order into the second and third answer boxes with only one dx or dy in each box. Then, enter...
Evaluate the surface integral 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 yj+3 k S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y 0 and x y 2 Evaluate the surface integral F dS for the given vector field F and the oriented surface...