2. Flux calculations: Set up the double integral for Js F.dA using cylindrical, spherical or shad...
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...
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = (x2, yz, zº) through the open-ended circular cylinder of radius 5 and height 4 with its base on the xy-plane and centered about the positive z-axis, oriented away from the z-axis. If necessary, enter 6 as theta. Flux = -MIT" dz de A= BE C= D= (b) Evaluate the integral. Flux = S]
1. Use cylindrical coordinates to SET UP the integral for the volume of the portion of the unit ball, 22 +232 + x2 < 1, above the plane z = 12 2. (a) Write in spherical coordinates the equations of the following surfaces: (i) x2 + y2 + x2 = 4 (ii) z = 3x2 + 3y2 (b) SET UP the integral in spherical coordinates for the volume of the solid inside the surface 22 + y2 + x2 =...
A) solve this integral in cylindrical coordinates. b) set up the integral in spherical coordinates (without solving) 10 points Compute the following triple integral: 1/ 1.32 + plav JD where D is the region given by V x2 + y2 <2<2. Hint: z= V x2 + y2 is a cone.
(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
3. About Flux: Suppose F-Ji + 2j-k and s is a region on the plane x + y-z-3. Distinguish the scenario where we can bypass the flux integral by simply computing F. A and the scenario where we have to integrate using the shadow method. Compute the flux. (a) S is a circle of radius 3 on the plane. O F.A Which method is appropriate? Compute the flux: O shadow method. 2 9 on the xy plane. (b) S is...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane. 4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
(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...
Set up, but do not evaluate, a triple integral in cylindrical coordinates that gives the volume of the solid under the surface z = x2 + y2, above the xy- plane, and within the cylinder x2 + y2 = 2y.
Oss4).Nor nal vectors po nt up e-zZxy across the curved sides of the surfa es-(xyz. z-cos y. y s: Find the flux of the vector field F= a Set up the integral that gives the flux as a double integral over a region R in the xy-plane. IIF.nds-IJO dA (Type exact answers.) Oss4).Nor nal vectors po nt up e-zZxy across the curved sides of the surfa es-(xyz. z-cos y. y s: Find the flux of the vector field F= a...